Factors / Multiples - ACT Math

Since we want a to be as large as possible, we want b to be as small as possible. The lowest possible value of b, then, is 4. If b is 4, then we can solve for a by setting up the equation:

4(a) = 96

96/4 = 24

If you divide the answer choices by 4, 5, and 6, 120 is the only choice that divides evenly by all three numbers.

The least comon multiple is the lowest multiple of all three numbers. 160 is 32x5, 16x10, and 8x20.

12 is the least common multiple of 4 and 6.

Find the multiples of 40, and find the smallest one that is divisible by 8 and 25.

To find the least common multiple of two numbers, if they are both prime, simply multiply the numbers.

Thus we get that

We could also write out the multiples of each number and see what numbers they have in common. The least common multiple will be the common number that appears first in both sets.

To find the lowest common multiply, we need to find the smallest value which is a factor of each of the three numbers. We know it has to be even from the factor of two. If we look at the value , the lowest multiple of that number is Since the other two values are also divisible by this number, that is the lowest common multiple.

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 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 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

GCF=greatest common factor. First find the factors of each number. So the factors for each number are

36: 1, 36, 2, 18, 3, 12, 4, 9, 6

64: 1, 64, 2, 32, 4, 16

144:1, 144, 2, 72, 3, 48, 4, 36, 6, 24, 8, 18, 9, 16, 12.

1, 2, and 4 are the only factors that are common to 36, 64, and 144. Since 4 is the greatest of these factors, it is the correct answer.

All three numbers are divisible by 2, 4, 6, and 12, but only 48 is divislbe by 24. Therefore, the greatest common factor of these three numbers is 12.

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.

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.

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.

There are two approaches to this question. You can either list all of the factors for each of the numbers given in the question and see which one is the greatest that the three have in common. The other approach is to check each of the three numbers in the question by the answer choices and see which is the greatest factor of all three numbers.

In this case:

Note that is a common factor of these numbers, but is obviously smaller than .

The greatest common factor is the largest factor that goes into both numbers. Begin by factoring each number:
:
.

The common facors are, , and the greatest of these is

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.

Prime numbers are by definition only divisible by themselves and 1.

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.