# 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
3 years, 1 month ago

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## Comments

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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.

- 3 years, 1 month ago

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

- 3 years, 1 month ago

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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?

- 3 years, 1 month ago

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

- 3 years, 1 month ago

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

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

- 3 years, 1 month ago

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but why is it 6??

- 3 years, 1 month ago

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Your question reads:

... 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....?

- 3 years, 1 month ago

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oh ok thanx !!

- 3 years, 1 month ago

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

- 3 years, 1 month ago

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No. $\quad \quad$

- 3 years, 1 month ago

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