Question

find the G.C.D of 605 and 935 by division method​​

Answer 1

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Approach 1.

Integer numbers prime factorization:

935 = 5 × 11 × 17;  

605 = 5 × 112;

Take all the common prime factors, by the lowest exponents.

Greatest (highest) common factor (divisor):  

gcf, gcd (935; 605) = 5 × 11 = 55;

Approach 2.

Euclid's algorithm:

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

935 ÷ 605 = 1 + 330;

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

605 ÷ 330 = 1 + 275;

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

330 ÷ 275 = 1 + 55;

Step 4. Divide the remainder from the step 2 by the remainder from the step 3:  

275 ÷ 55 = 5 + 0;

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

55 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 (935; 605) = 55 = 5 × 11;

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