I'ma teacher at a local Middle School and I would like the answers for the following questions.

What is the greatest common factor for..

546 and 780

156 and 732

285 and 399

168 and 300

2,103 and 9,945

204 and 306

170 and 272

40 and 109

483 and 759

324 and 432

1,492 and 1,924

Hi,

The usual way to find the greatest common factor, GCF (sometimes called the greatest common divisor) is to first find prime factorization of the numbers. For your first pair, 546 and 780,

546 = 2x3x7x13 and

780 = 22x3x5x13
Find the highest power of each prime that divdes both numbers and then the product of these powers is the GCF. Thus the GCF of 546 and 780 is 2x3x13 = 78.

Likewise for 2,103 and 9,945

2103=3x701

9945 = 32x5x13x17
Only 3 divides both 2103 and 9945 and thus their GCF is 3.

If you know the Euclidean Algorithm you can use it to find the GCF's.

By the Euclidean Algorithm:

780 and 546:

780 = 546(1) + 234
546 = 234(2) + 78 -- 78 is the last non-zero remainder, so 78 is the GCD
234 = 78(3) + 0

2,103 and 9,945:

9,945 = 2,103(4) + 1,533
2,103 = 1,533(1) + 570
1,533 = 570(2) + 393
570 = 393(1) + 177
393 = 177(2) + 39
177 = 39(4) + 21
39 = 21(1) + 18
21 = 18(1) + 3
18 = 3(6) + 0

Thus the GCF is 3

Cheers,
Leeanne and Penny
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