What is the greatest common factor of 210 and 490?

Answer 1

The greatest common factor of two or more numbers can be found by prime factorization method.

In this method each number is expressed as the product of prime factors and then we look for what is common?

P.F. of 210 = 2 x 3 x 5 x 7

P.F. of 490 = 2 x 5 x 7 x 7

As we can see that 2 x 5 x 7 is the greatest number which is common in P.F. of both numbers.

So, GCF(210, 490) = 2 x 5 x 7 = 70.

Another method of finding GCF is by applying Euclid's Division Lemma:

Statement of Euclid's Lemma: Given positive integers a and b(a>b), there exist unique integers q and r such that: a = bq + r.

Now how we apply Euclid's division lemma?

First of all the lemma is applied for the given two numbers.

490 = 210 x 2 + 70.

If remainder is not zero then the divisor becomes dividend and the remainder becomes divisor for the next step, the process is continued till remainder obtained is not zero.

70 = 210 x 3 + 0.(Remainder is zero)

The last divisor is the GCF. So, GCF is 70.

Answer 2

The GCF is 70.