What is the greatest number that will divide 22, 90, and 150 with the same…
2025
What is the greatest number that will divide 22, 90, and 150 with the same remainder in each case?
- A.
4
- B.
6
- C.
10
- D.
25
Attempted by 129 students.
Show answer & explanation
Correct answer: A
Key idea: A number that leaves the same remainder when dividing several numbers must divide the differences between those numbers.
Compute the pairwise differences: 90 − 22 = 68, 150 − 90 = 60, and 150 − 22 = 128.
Find the greatest common divisor (GCD) of 68, 60, and 128.
Compute GCD stepwise: gcd(68, 60) = gcd(60, 8) = gcd(8, 4) = 4. Then gcd(4, 128) = 4.
Therefore the largest number that divides 22, 90, and 150 leaving the same remainder is 4.
Answer: 4