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

Easy Math Editor

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`2 \times 3`	$2 \times 3$
`2^{34}`	$2^{34}$
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Comments

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.

Pi Han Goh - 3 years, 5 months ago

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

erica phillips - 3 years, 5 months 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?

Pi Han Goh - 3 years, 5 months ago

@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 - 3 years, 5 months ago

@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 - 3 years, 5 months ago

@Pi Han Goh – but why is it 6??

erica phillips - 3 years, 5 months ago

@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 - 3 years, 5 months ago

@Pi Han Goh – oh ok thanx !!

erica phillips - 3 years, 5 months ago

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

erica phillips - 3 years, 5 months ago

@Erica Phillips – No. $\quad \quad$

Pi Han Goh - 3 years, 5 months ago

Math	Appears as
Remember to wrap math in `\(` ... `\)` or `\[` ... `\]` to ensure proper formatting.
`2 \times 3`	$2 \times 3$
`2^{34}`	$2^{34}$
`a_{i-1}`	$a_{i-1}$
`\frac{2}{3}`	$\frac{2}{3}$
`\sqrt{2}`	$\sqrt{2}$
`\sum_{i=1}^3`	$\sum_{i=1}^3$
`\sin \theta`	$\sin \theta$
`\boxed{123}`	$\boxed{123}$