Question

find G.C.D of78 and 455

Answer 1

Step 1. Divide the larger number by the smaller one:  

455 ÷ 78 = 5 + 65;

Step 2. Divide the smaller number by the above operation's remainder:  

78 ÷ 65 = 1 + 13;

Step 3. Divide the remainder from the step 1 by the remainder from the step 2:  

65 ÷ 13 = 5 + 0;

At this step, the remainder is zero, so we stop:  

13 is the number we were looking for, the last remainder that is not zero.  

This is the greatest common factor (divisor).

Greatest (highest) common factor (divisor):  

gcf, gcd (455; 78) = 13;

Answer 2

SOLUTION . Integer numbers prime factorization:

455 = 5 × 7 × 13;  

78 = 2 × 3 × 13;

So, consider all the common prime factors, by the lowest exponents.

Greatest (highest) common factor (divisor)  will be

gcf, gcd (455; 78) = 13;