What will be remainder when 87 * 137 is divided by 17?
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What will be remainder when 87 * 137 is divided by 17?
- A.
0
- B.
1
- C.
2
- D.
3
Attempted by 8 students.
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Correct answer: C
Solution:
Compute each factor modulo 17 and use the fact that the product of residues gives the residue of the product.
Find remainder of 87 ÷ 17: 87 − 17 × 5 = 2, so 87 ≡ 2 (mod 17).
Find remainder of 137 ÷ 17: 137 − 17 × 8 = 1, so 137 ≡ 1 (mod 17).
Multiply the residues: 2 × 1 = 2, so 87 × 137 ≡ 2 (mod 17).
Answer: The remainder is 2.