Question

What is the greatest common factor of 90, 126, 180 and 990?

Answer 1

9514 1404 393

Answer:

  18

Step-by-step explanation:

90 = 18·5

126 = 18·7

180 = 18·10

990 = 18·55

The greatest common factor of these numbers is 18.

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Comment on the GCF

It can be useful to know Euclid's algorithm for finding the GCF:

1. Determine the remainder from dividing the larger number by the smaller.
2. If the remainder is zero, the smaller number is the GCF. If the remainder is non-zero, use it to replace the larger number and repeat from step 1.

For example, 126 mod 90 = 36; 90 mod 36 = 18; 36 mod 18 = 0, so 18 is the GCF of 126 and 90. (The modulo function 'mod' returns the remainder from division.)