Question

The product of two 2-digit numbers is 2444. If the product of their unit digits is 14 and tens digits is 20, then what are the two numbers?

Answer 1

Given that the product of units digits of the two 2 - digit numbers is 14. So first we have to factorise 14 as product of two 1 - digit numbers.

14 can only be factorised as two 1 - digit numbers as follows,

$\longrightarrow\sf{14=2\times7}$

Hence we get the unit digit of one among the two 2 - digit numbers is 2 and that of the other is 7.

Given that the product of their tens digits is 20. Like 14, we have to factorise 20 as product of two 1 - digit numbers too.

20 can also be factorised as two 1 - digit numbers only as the following,

$\longrightarrow\sf{20=4\times5}$

Hence we get the tens digit of one among the two 2 - digit numbers is 4 and that of the other is 5.

Case 1:-

Let the numbers be 42 and 57.

$\longrightarrow\sf{42\times57=2394}$

Hence 42 and 57 are not the numbers.

Case 2:-

Let the numbers be 47 and 52.

$\longrightarrow\sf{\underline{\underline{47\times52=2444}}}$

Hence 47 and 52 are the numbers.