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What is the greatest common factor of 374 and 638?

Guest Feb 19, 2015

Best Answer 

 #1
avatar+17745 
+5

The greatest common factor is 22.

22 x 17 = 374  and  22 x 29 = 638.

One way to find this to to use the Euclidean algorithm (named in honor of Euclid).

Divide the smaller number into the larger number, and look at the remainder:

638 ÷ 374  =  1, with a remainder of 264  (Actually, you don't care about the quotient, just the remainder).

Since the remainder isn't 0, divide the remainder into the divisor:

374 ÷ 264  =  1, with a remainder of 110.

Since the remainder still isn't 0, divide the remainder into the divisor:

264 ÷ 110  =  2, with a remainder of 44.

Since the remainder still isn't 0, divide the remainder into the divisor:

110 ÷ 44  =  2, with a remainder of 22.

Since the remainder still isn't 0, divide the remainder into the divisor:

44 ÷ 22  =  2, with a remainder of 0.

Now, when the remainder is 0, you are done and your answer (the greatest common factor) is the last divisor; so the greatest common factor is 22.

geno3141  Feb 19, 2015
 #1
avatar+17745 
+5
Best Answer

The greatest common factor is 22.

22 x 17 = 374  and  22 x 29 = 638.

One way to find this to to use the Euclidean algorithm (named in honor of Euclid).

Divide the smaller number into the larger number, and look at the remainder:

638 ÷ 374  =  1, with a remainder of 264  (Actually, you don't care about the quotient, just the remainder).

Since the remainder isn't 0, divide the remainder into the divisor:

374 ÷ 264  =  1, with a remainder of 110.

Since the remainder still isn't 0, divide the remainder into the divisor:

264 ÷ 110  =  2, with a remainder of 44.

Since the remainder still isn't 0, divide the remainder into the divisor:

110 ÷ 44  =  2, with a remainder of 22.

Since the remainder still isn't 0, divide the remainder into the divisor:

44 ÷ 22  =  2, with a remainder of 0.

Now, when the remainder is 0, you are done and your answer (the greatest common factor) is the last divisor; so the greatest common factor is 22.

geno3141  Feb 19, 2015

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