# Square root

hello , I really urgently need your help in this problem The product of 2 natural nos. is 15120 and their HCF is 6.Find how many such pairs exist.

Pls help me to find the solution to this problem

Note by Erica Phillips
6 months, 2 weeks ago

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Hint: Let $$A$$ and $$B$$ be the 2 integers. Show that $$\dfrac A6$$ and $$\dfrac B6$$ are coprime.

Hint 2: Factorize $$\dfrac{15120}{6\times6}$$ into product of 2 coprime posiitve integers.

- 6 months, 2 weeks ago

I have factorized 420 by 7 and 5 and then??

- 6 months, 2 weeks ago

We know that $$A/6$$ and $$B/6$$ are coprime positive integers, and that $$A/6 \times B/6 = 420$$.

So we want to find 2 coprime positive integers that give a product of 420.

For example $$1\times 420$$, $$4\times 105$$, $$3\times35$$, $$15 \times 7$$.

Is there any other way?

- 6 months, 2 weeks ago

I just wanna ask why have you divided A and B by 6 to prove that they are co prime??

- 6 months, 2 weeks ago

Both $$A$$ and $$B$$ are divisible by 6, right?

Are there any other larger integer that must divide both $$A$$ and $$B$$?

- 6 months, 2 weeks ago

but why is it 6??

- 6 months, 2 weeks ago

... The product of 2 natural nos. is 15120 and their HCF is 6

In other words, the largest integer that divides both $$A$$ and $$B$$ is....?

- 6 months, 2 weeks ago

oh ok thanx !!

- 6 months, 2 weeks ago

so u wanna say that 1420,4105,335,157 are the probable pairs.right??

- 6 months, 2 weeks ago

No. $$\quad \quad$$

- 6 months, 2 weeks ago