Q:

# What is the greatest common factor for the numbers 16 and 40?

A:

Eight is the greatest common factor for the numbers 16 and 40. The factors of a particular number are those numbers that divide into it evenly, leaving no remainder. The greatest common factor between two numbers is the highest number that divides evenly into both of them.

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The factors of 16 are 1, 2, 4, 8 and 16. The factors of 40 are 1, 2, 4, 5, 8, 10, 20 and 40. One, two, four and eight are the factors that 16 and 40 have in common, and eight is the largest. Finding the greatest common factor is also done with prime factorization. The prime factorization of 16 is 2^4, and the prime factorization of 40 is 2^3 x 5. Because the only common prime factor is two and the exponent in common is three, 2^3, or 8, is the greatest common factor.

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