What is the greatest common factor of 25 and 42?

Answer 1

Answer: 1. One way to determine the greatest common factor is to find all the factors of the numbers and compare them.

The factors of 25 are 1, 5, and 25.

The factors of 42 are 1, 2, 3, 6, 7, 14, 21, and 42.

The only common factor is 1. Therefore, the greatest common factor is 1, which means the numbers are relatively prime.

The greatest common factor can also be calculated by identifying the common prime factors and multiplying them together.

The prime factors of 25 are 5 and 5.

The prime factors of 42 are 2, 3, and 7.

There are no prime factors in common, so the numbers are relatively prime, which means the greatest common factor is 1.

Another way to approach this is to look at the difference between 25 and 42, which is 17. The greatest common factor of two numbers cannot be larger than the difference between the two numbers and must be a factor of the difference between the numbers. Since 17 is a Prime number, the greatest common factor must be either 1 or 17. Neither 25 nor 42 are divisible by 17, so the greatest common factor is 1. This is a useful shortcut if you notice that the difference between the two numbers is a prime number.

Answer 2

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Answer 3

1