Factors / Multiples - ACT Math
Card 0 of 20
Which of the following lists all the factors of 36?
Which of the following lists all the factors of 36?
1, 2, 3, 4, 6, 9, 12, 18, 36 are all of the factors of 36.
1, 2, 3, 4, 6, 9, 12, 18, 36 are all of the factors of 36.
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The number 9 is the second smallest integer with 3 factors, 1, 3, and 9. What is the sum of the factors of the smallest integer with only 3 factors?
The number 9 is the second smallest integer with 3 factors, 1, 3, and 9. What is the sum of the factors of the smallest integer with only 3 factors?
Here we must do two things. First we must find the smallest integer with 3 factors, then we must add those factors so that we can obtain our answer.
Looking at numbers less than 9 with only 3 factors, the only possibility is the number 4, whose factors are 1, 2, and 4.
The sum of these factors is 1 + 2 + 4 = 7
Here we must do two things. First we must find the smallest integer with 3 factors, then we must add those factors so that we can obtain our answer.
Looking at numbers less than 9 with only 3 factors, the only possibility is the number 4, whose factors are 1, 2, and 4.
The sum of these factors is 1 + 2 + 4 = 7
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What are the factors of the number 12?
What are the factors of the number 12?
The factors of a number are all the numbers that can be multiplied by an integer to get that number.
The factors of a number are all the numbers that can be multiplied by an integer to get that number.
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If a and b are both factors of 64, which of the following could be a * b?
If a and b are both factors of 64, which of the following could be a * b?
The factors of 64 are: 1,2,4,8,16,32,64. Therefore, 128 could be the product of 16 and 8.
The factors of 64 are: 1,2,4,8,16,32,64. Therefore, 128 could be the product of 16 and 8.
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Which of the following is not a factor of 52?
Which of the following is not a factor of 52?
Listing all the factors of 52: 1,2,4,13,26,52.
3 is not one of the factors.
Listing all the factors of 52: 1,2,4,13,26,52.
3 is not one of the factors.
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What is the sum of the greatest common factor (GCF) and the least common multiple (LCM) of 
, 
, and 
?
What is the sum of the greatest common factor (GCF) and the least common multiple (LCM) of
: the largest factor that divides evenly into all numbers
: the smallest non-zero number that divides evenly into all numbers. If you are unable to find the GCF, then it is 1.
Prime factorize all numbers:
, because all numbers are relatively prime.
Therefore, 
.
Prime factorize all numbers:
Therefore,
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What is the power of the greatest prime factor of 
?
What is the power of the greatest prime factor of
To get the answer to this question, just carefully prime factor the value 
:
First, 
Now, 
For 
, begin by dividing by 
:
Now, this is a bit trickier for 
. This happens to be divisible by 
:
also is divisible by 
:
Thus, your total answer is:
To get the answer to this question, just carefully prime factor the value
First,
Now,
For
Now, this is a bit trickier for
Thus, your total answer is:
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How many factors are there for the number 
?
How many factors are there for the number
To find the number of factors of a given number, the easiest thing to do is to make a table of the factors, starting with 
and that number. So, for 
, we get:
At this point, things begin to repeat. Thus, the total number of factors is 
.
To find the number of factors of a given number, the easiest thing to do is to make a table of the factors, starting with
At this point, things begin to repeat. Thus, the total number of factors is
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What is the median value of the factors of 
?
What is the median value of the factors of
To find the number of factors of a given number, the easiest thing to do is to make a table of the factors, starting with 
and that number. So, for 
, we get:
At this point, the values begin to repeat. This means that there are an even number of factors. At the "middle" of the list, we find 
and 
. To find the median of the list, you merely need to take the average of these two numbers:
To find the number of factors of a given number, the easiest thing to do is to make a table of the factors, starting with
At this point, the values begin to repeat. This means that there are an even number of factors. At the "middle" of the list, we find
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What is the probability of selecting a prime number out of the following set?
{2, 6, 9, 17, 21, 47, 63, 71, 81}
What is the probability of selecting a prime number out of the following set?
{2, 6, 9, 17, 21, 47, 63, 71, 81}
Probability is determined by dividing favorable outcomes, by possible outcomes. As there are 9 numbers in the given set, the number of possible outcomes is 9. In the given set, only 2, 17, 47 and 71 are prime numbers (divisible only by 1 and itself). Thus, there are 4 favorable outcomes, yielding a probability of 4/9.
Probability is determined by dividing favorable outcomes, by possible outcomes. As there are 9 numbers in the given set, the number of possible outcomes is 9. In the given set, only 2, 17, 47 and 71 are prime numbers (divisible only by 1 and itself). Thus, there are 4 favorable outcomes, yielding a probability of 4/9.
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How many prime numbers between 20 and 40 are divisible by 9?
How many prime numbers between 20 and 40 are divisible by 9?
Prime numbers are by definition only divisible by themselves and 1.
Prime numbers are by definition only divisible by themselves and 1.
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How many prime numbers are between 40 and 60?
How many prime numbers are between 40 and 60?
A prime number is a number that is only divisible by 1 and the number itself (examples include 3, 11, 19). The prime numbers between 40 and 60 are 41, 43, 47, 53, and 59.
A prime number is a number that is only divisible by 1 and the number itself (examples include 3, 11, 19). The prime numbers between 40 and 60 are 41, 43, 47, 53, and 59.
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How many integers between 2 and 61 are prime numbers, inclusive?
How many integers between 2 and 61 are prime numbers, inclusive?
The key word is “inclusive.” The answer is 18 prime numbers. If you answered 16, you did not include 2 and 61 as prime numbers. If you answered 17, you only included one of the outer limits in the range. If you answered 15, you did not include the outer limits, 2 and 61, as prime numbers and miscounted. There are 18 prime numbers between 2 and 61 when you include the range’s limits.
The key word is “inclusive.” The answer is 18 prime numbers. If you answered 16, you did not include 2 and 61 as prime numbers. If you answered 17, you only included one of the outer limits in the range. If you answered 15, you did not include the outer limits, 2 and 61, as prime numbers and miscounted. There are 18 prime numbers between 2 and 61 when you include the range’s limits.
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Which of the following sets of numbers contain all prime numbers?
Which of the following sets of numbers contain all prime numbers?
A prime number can only be divided by the number itself and 1.
A prime number can only be divided by the number itself and 1.
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What is the greatest common factor of 36,108, and 180?
What is the greatest common factor of 36,108, and 180?
We can find the greatest common factor of a series of numbers by performing the prime factorization of each number. The greatest common factor will be the product of the combinations of prime factors that each number has in common. 36 can be factorized to 22 * 32.108 can be factorized to 22 * 33. 180 can be factorized to 32 * 22 * 5. The greatest common prime factorization is 22 * 32, the product of which is 36. So 36 is the greatest common factor. Remember that 22 * 33 = 22 * 32 * 3.
We can find the greatest common factor of a series of numbers by performing the prime factorization of each number. The greatest common factor will be the product of the combinations of prime factors that each number has in common. 36 can be factorized to 22 * 32.108 can be factorized to 22 * 33. 180 can be factorized to 32 * 22 * 5. The greatest common prime factorization is 22 * 32, the product of which is 36. So 36 is the greatest common factor. Remember that 22 * 33 = 22 * 32 * 3.
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What is the greatest common factor of 56 and 68?
What is the greatest common factor of 56 and 68?
The factors are as follows:
56: 1,2,4,7,8,14,28,56
68, 1,2,4,17,34,68
The greatest factor that both numbers are divisible by is 4.
The factors are as follows:
56: 1,2,4,7,8,14,28,56
68, 1,2,4,17,34,68
The greatest factor that both numbers are divisible by is 4.
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What is the greatest common factor of 72 and 84?
What is the greatest common factor of 72 and 84?
Factors are numbers that can divide evenly into larger numbers. The factors of 72 are 36, 24, 18, 12, 9, 8, 6, 4, 3, and 2. The factors of 84 are 42, 28, 21, 14, 12, 7, 6, 4, 3, and 2. Thefore, the greatest common factor is 12.
Factors are numbers that can divide evenly into larger numbers. The factors of 72 are 36, 24, 18, 12, 9, 8, 6, 4, 3, and 2. The factors of 84 are 42, 28, 21, 14, 12, 7, 6, 4, 3, and 2. Thefore, the greatest common factor is 12.
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What is the greatest common factor of 49, 91, and 119?
What is the greatest common factor of 49, 91, and 119?
The greatest common factor is the largest integer that divides without remainder into a set of integers. In this case, 1 and 7 are both common factors, but 7 is the greatest common factor.
The greatest common factor is the largest integer that divides without remainder into a set of integers. In this case, 1 and 7 are both common factors, but 7 is the greatest common factor.
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What is the greatest common factor of 55, 165, and 220?
What is the greatest common factor of 55, 165, and 220?
The greatest common factor is the largest factor that the given numbers have in common. 5 is a common factor, but it is not the greatest one; 11 and 20 are not common factors to the given numbers; however, 55 is a common factor of the given three numbers and is the greatest one at that.
The greatest common factor is the largest factor that the given numbers have in common. 5 is a common factor, but it is not the greatest one; 11 and 20 are not common factors to the given numbers; however, 55 is a common factor of the given three numbers and is the greatest one at that.
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What is the greatest common factor of 30, 90, and 120?
What is the greatest common factor of 30, 90, and 120?
The greatest common factor can most easily be found by plugging in answers from your answer choices, a good strategy with these types of problems is to simply guess and check using your largest answer, in this case, we see that 30 is immediately the GCF for these three numbers
The greatest common factor can most easily be found by plugging in answers from your answer choices, a good strategy with these types of problems is to simply guess and check using your largest answer, in this case, we see that 30 is immediately the GCF for these three numbers
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