Question

14 is the GCF of a number M and 210. What are possible values of M?

Answer 1

Hello,

we know that to find the GCF we descompose the numbers and then we multiply the common terms with the lowest exponent. So we first descompose 210:

210 | 2

105 | 3

35 | 5

7 | 7

1

210= 2x3x5x7

Now one possible solution is 14 because:

14 | 2

7 | 7

1

As you can see 2 and 7 are common terms, so:

GCF= 2x7

GCF=14 --> It's correct

Then, if we analyze it, we'll realize that we have an infinitive number of solutions. The only requirement is that "M" must have 2 and 7 when we descompose it.

For example:

M= 2²x7x3x11

M=924

924 is another possible solution, it doesn't matter if 2 or 7 repeat, since I said the GCF is the multiplication of the common terms with the LOWEST exponent. That's all.

Explanation: