85.8k views
4 votes
Example 16: Find the greatest number that will divide 113, 135 and 160 leaving remainders 5, 3 and 4, respectively.​

User Ella Cohen
by
7.5k points

1 Answer

3 votes

Answer:

12

Explanation:

If 113 divided by a number leaves a remainder of 5, then we need to find the prime factorization of 108.

If 135 divided by a number leaves a remainder of 3, then we need to find the prime factorization of 132.

If 160 divided by a number leaves a remainder of 4, then we need to find the prime factorization of 156.

108 = 2² × 3³

132 = 2² × 3 × 11

156 = 2² × 3 × 13

The GCF of 108, 132, and 156 is common factors with lower exponent.

GCF = 2² × 3 = 12

Answer: 12

User Shaylh
by
7.6k points