Question

when 2388, 4309 and 8151 are divided by a certain 3 digit number, the remainder in each case is the same. the remainder is?​

Answer 1

Step-by-step explanation:

Given When 2388, 4309 and 8151 are divided by a certain 3 digit number, the remainder in each case is the same. the remainder is?

• We need to find the greatest common factor hcf of (4309 – 2388)(8151 – 4309)(8151 – 2388) will be 1921, 3842 and 5763
• So factors of 1921 = 17 x 113
• 3842 = 2 x 17 x 113
• 5763 = 3 x 17 x 113
• So hcf will be 17 x 113
• Now 1921 = 17 x 113
• Now the three digit number is 113. So numbers are
• 2388 = (113 x 21) + 15
• 4309 = (113 x 38) + 15
• 8151 = (114 x 72) + 15
• Therefore the required number is 113 and remainder is 15