Question

What is the greatest number that divides 1803 and 2028
a remainder of 3 in each case ? ​

Answer 1

_____Answer _________

Here, we need to find differences between the given numbers. If two numbers give the same remainder when divided by some other number, then their difference must give a remainder of zero when divided by that number.

Our numbers here are 91−43=48,183−91=92,183−43=140

So we have the set of numbers {48,92,140} and we want to know the biggest number that divides all these numbers.

So,

48=2×2×2×3

92=2×2×23

140=2×2×5×7

The greatest common divisor of {48,92,140} is 4.

So, answer is 4.

Answer 2

Step-by-step explanation:

1803-3=1800

2028-3=2025

1800=2×2×2×3×3×5×5

2025=3×5×5×5×5

HCF=3×5×5

=75