Question
Download Solution PDFFind the remainder when 179 × 172 × 173 is divided by 17.
Answer (Detailed Solution Below)
Detailed Solution
Download Solution PDFGiven:
Find the remainder when 179 × 172 × 173 is divided by 17.
Formula used:
Using the property of modular arithmetic:
(a × b) mod m = [(a mod m) × (b mod m)] mod m
Calculation:
179 mod 17 = 179 - (17 × 10) = 179 - 170 = 9
172 mod 17 = 172 - (17 × 10) = 172 - 170 = 2
173 mod 17 = 173 - (17 × 10) = 173 - 170 = 3
⇒ 179 × 172 × 173 mod 17 = (9 × 2 × 3) mod 17
⇒ 54 mod 17 = 54 - (17 × 3) = 54 - 51 = 3
∴ The correct answer is option 3.
Last updated on Jul 22, 2025
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