Question

What is the greatest number by which if 1023 and 750 be divided 3 and 2 are left as remainders ?

Answer 1

Given, when 1023 and 750 are divided by the greatest number will leave 3 and 2 as the remainder.

Then, the numbers which are perfectly divisible by the greatest number are (1023 -3)=1020 and (750-2)=748.

Therefore, 1020 and 748 are perfectly divisible by the greatest number.

"Greatest number" means the greatest common factor (GCF).
 
Then, we need to find the greatest common factor of 1020 and 748.

1020= 2*2*3*5*17

748=2*2*11*17

GCF of 1020 and 478 = 2*2*17=68

The required greatest number is 68 by which if 1023 and 750 are divided 3 and 2 will be left as the remainder.


Answer : The required greatest number is 68.