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What is the greatest common factor of 21 and 63?

Answer 1

#HCF(21,63)=gcd(a,b)=21#

By definition, #a# is a factor of #b# if it can divide perfectly into #b# without leaving a remainder.

That is, #a|biff EEk in ZZ # such that #a/b=k or a=kb#.

So hence we may list all the factors of each number and see which are common to both sets and then select the highest one that is common.

Factors of #21={1,3,7,21}#

Factors of #63={1,3,7,9,21,63}#

#therefore #the highest common factor (HCF) is #21#.

Note: Some texts also refer to this as the greatest common divisor (gcd), and if the numbers are very big, we may use Euclid's Algorithm to find it.

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Answer 2

Emery Allen

#21#

Both #21# and #63 = 3 * 21# are divisible by #21# and #21# has no greater factor, so this must be the greatest common factor.

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Answer 3

Gianna Caruso

The greatest common factor (GCF) of 21 and 63 is 21.

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Answer from HIX Tutor

When evaluating a one-sided limit, you need to be careful when a quantity is approaching zero since its sign is different depending on which way it is approaching zero from. Let us look at some examples.