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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 1 year, 7 months 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.

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

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?

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

@Erica Phillips – Both $A$ and $B$ are divisible by 6, right?

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

@Pi Han Goh – but why is it 6??

@Erica Phillips – 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....?

@Pi Han Goh – oh ok thanx !!

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

@Erica Phillips – No. $\quad \quad$

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Remember to wrap math in $</span> ... <span>$ or $</span> ... <span>$ to ensure proper formatting.`2 \times 3`

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`\sqrt{2}`

`\sum_{i=1}^3`

`\sin \theta`

`\boxed{123}`

## Comments

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TopNewestHint: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.Log in to reply

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

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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?

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Log in to reply

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

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

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Log in to reply

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

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420,4105,335,157 are the probable pairs.right??Log in to reply

$\quad \quad$

No.Log in to reply