What is the Greatest Common Factor of 17 and 51?

Question

Please help me

Answer 1

Every positive integer has "factors" that are multiplied to produce that number.  For example, the number 10 has factors of 1, 2, 5 and 10.

 

Some important information uses "prime factors."  Since prime numbers begin with 2 (and 10 is not prime), the prime factors of 10 are 2 and 5,

 

When a number has several prime factors, it is important to recognize the fact that they occur multiple times.  So, the prime factors of 45 are 3, 3, and 5.

 

For this problem, the factors are:

 17:     1, 17

 51:     1, 3, 17, 51

 

The Greatest Common Factor is the greatest number that is common (that is, in both lists).  It is 17.

Answer 2

Since 17 is a factor of itself and of 51 -- which is 3 x 17 -- then the greatest possible common factor is 17!

Answer 3

17 is prime, that is it can be written only as 17 = 1(17); and 51 is composite (can be written as 51 = 3(17)); therefore, gcf(17,51) = 17

Answer 4

17=17 (prime)

51=3*17 (51 is divisible by 3 because 5+1=6 and 6 is divisible by 3)

GCF=17