What is the GCF of 35 and 49?

1 Answer
George C.
Nov 9, 2016

7

Explanation:

One simple but sometimes slow method for finding the GCF of two positive numbers goes as follows:

  • If the two numbers are equal then they are equal to the GCF.

  • Otherwise replace the larger number with the result of subtracting the smaller number from it.

In our example:

  • Start with 35 and 49

  • Since they are unequal, subtract 35 from 49, getting 14

  • Our two numbers 35 and 14 are unequal, so replace 35 with 35-14 = 21.

  • 21 and 14 are unequal, so replace 21 with 21-14 = 7.

  • 14 and 7 are unequal, so replace 14 with 14-7 = 7.

  • 7 and 7 are equal, so they are our GCF.

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