What Is the Greatest Common Factor of 42 and 96?

The greatest common factor of 42 and 96 is 6. Here's how we can find it:

First, we'll list the factors of 42: 1, 2, 3, 6, 7, 14, 21, 42.

Next, we'll list the factors of 96: 1, 2, 3, 4, 6, 8, 12, 16, 24, 32, 48, 96.

As we can see, the greatest common factor of 42 and 96 is 6.

Suggestion: Factors Influence

The smallest number that 42 and 96 have in common is 24. Although 42 is divisible by 6 and 96 is divisible by 8, 24 is the smallest number that is divisible by both 6 and 8. Therefore, 24 is the smallest number that 42 and 96 have in common.

It is important to note that the smallest number that 42 and 96 have in common is not necessarily the lowest common multiple (LCM) of the two numbers. The LCM of 42 and 96 is 1248, which is significantly larger than 24. In fact, the LCM of any two numbers is always going to be bigger than the smallest number that the two numbers have in common. However, the LCM is still a good way to find the smallest number that two numbers have in common, because it will always be divisible by both numbers.

To find the LCM of two numbers, you can use the greatest common divisor (GCD) method. To do this, you first need to find the GCD of the two numbers. The GCD of 42 and 96 is 6. Once you have the GCD, you can divide it into both numbers to get their respective quotients. In this case, the quotients would be 7 and 16. Then, you would simply multiply the two quotients to get the LCM, which would be 112 in this case.

However, as previously mentioned, the LCM is not always the smallest number that two numbers have in common. In fact, the LCM is only the smallest number that two numbers have in common if one of the numbers is a multiple of the other. This is not the case with 42 and 96, which is why the LCM is not 24.

It is also worth mentioning that the smallest number that two numbers have in common is not always the same as the greatest common divisor (GCD) of the two numbers. The GCD of 42 and 96 is 6, but as previously mentioned, the smallest number that 42 and 96 have in common is 24. The GCD is the biggest number that can divide into both numbers evenly, but it is not necessarily the smallest number that the two numbers have in common.

In conclusion, the smallest number that 42 and 96 have in common is 24. This is because 24 is divisible by both 6 and 8, which are the two smallest factors of 42 and 96, respectively. It is

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There are a few different ways to interpret this question, so we will explore a few different answer possibilities.

One way to approach this question is to consider the prime factorization of each number. 42 can be written as 2 x 3 x 7, and 96 can be written as 2 x 2 x 2 x 2 x 2 x 3. The largest number that these two numbers have in common is 2 x 3, or 6.

Another way to look at this question is to consider the place value of each digit in the numbers 42 and 96. The digit 9 in 96 represents 9 tens, or 90. The digit 4 in 42 represents 4 tens, or 40. The largest number that these two numbers have in common is 40.

A third way to interpret this question is to consider the numbers in base 10 and base 2. In base 10, the largest number that 42 and 96 have in common is 10. In base 2, the largest number that 42 and 96 have in common is 100.

Ultimately, the answer to this question depends on how it is interpreted.

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