HCF and LCM via prime factorisation MCQs

Q1. What is the greatest number which divides 102 and 148 and leaves remainders 6 and 4?

• A.2
• B.4
• C.96
• D.48

Answer: D. 48

Q2. What is the greatest number which divides 138 and 148 and leaves remainders 6 and 4?

• A.132
• B.8
• C.12
• D.2

Answer: C. 12

Given 138, 148, 6, 4, asked for What is the greatest number which divides 138 and 148 and leaves remainders 6 and 4?. By midpoint corresponds to m = n = 1. midpoint corresponds to m = n = 1 → hence answer = 12. the section formula gives the dividing point of (x1,y1) and (x2,y2) in ratio m:n as ((m x2 + n x1)/(m + n), (m y2 + n y1)/(m + n)). Hence option C) 12. Others fail: option A) '132' misses the point - Wrong: a common multi-step slip gives this; option B) '8' is wrong because Wrong: uses an incorrect intermediate value.

Q3. What is the greatest number which divides 162 and 232 and leaves remainders 6 and 4?

• A.2
• B.4
• C.12
• D.156

Answer: C. 12