What is a compatible number of 75 and 26?

Question

Mathematics

Terrance Wong

15 May, 00:58

What is a compatible number of 75 and 26?

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Answers (1)

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Sloane Hunt · 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 26 are 1, 2, 13, and 26.

The factors of 48 are 1, 2, 3, 4, 6, 8, 12, 16, 24, and 48.

The factors of 75 are 1, 3, 5, 15, 25, and 75.

The only common factor is 1. Therefore, the greatest common factor is 1

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

The prime factors of 26 are 2 and 13.

The prime factors of 48 are 2, 2, 2, 2, and 3.

The prime factors of 75 are 3, 5, and 5.

The are no prime factors in common, so the greatest common factor is 1.

Another way to approach this is to look at the differences between the numbers. The difference between 26 and 48 is 22. The difference between 48 and 75 is 27. The greatest common factor of two or more numbers cannot be larger than the smallest difference between the numbers. The greatest common factor of 26, 48, and 75 must also be a factor of the differences between the numbers. So, the greatest common factor of 22 and 27 is also the greatest common factor of 26, 48, and 75. The greatest common factor of 22 and 27 is 1, so the greatest common factor of 26, 48, and 75 is also 1.