Question

Find two digit numbers which have gcd=6 and product=2880

Answer 1

SOLUTION

TO DETERMINE

Two digit numbers which have gcd=6 and product=2880

EVALUATION

Here it is given that gcd of the numbers = 6

Let the numbers are 6m and 6n

So by the given condition

$\sf{6m \times 6n = 2880}$

$\implies \: \sf{36mn = 2880}$

$\implies \: \sf{mn = 80}$

Since all the numbers to be determined are two digit numbers

So

• m = 5 , n = 16

• m = 8 , n = 10

• m = 10 , n = 8

• m = 16 , n = 5

So the required two digit numbers are

• 30 , 96

• 48 , 60

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