Example 1 · level 1
A number when divided by 55 leaves remainder 46. What is the remainder when the same number is divided by 11?
Show solution
- N = 55k + 46, and 55k is divisible by 11.
- 46 ÷ 11 leaves 2.
Answer: 2
SSC & BANK EXAMS: QUANTITATIVE APTITUDE · NUMBER SYSTEM
Remainders
Remainder of a product = product of remainders (then take the remainder again). If N leaves r on dividing by D and d divides D, N ÷ d leaves r ÷ d’s remainder.
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Worked examples
Example 2 · level 2
What is the remainder when 36 × 58 × 41 is divided by 9?
Show solution
- Remainders on dividing by 9: 0, 4, 5.
- 0 × 4 × 5 = 0.
- 0 ÷ 9 leaves 0.
Answer: 0
Example 3 · level 3
What is the remainder when 7^159 is divided by 5?
Show solution
- 7^4 ÷ 5 leaves 1.
- 7^159 = (7^4)^39 × 7^3.
- Remainder = 1 × 7^3 mod 5 = 3.
Answer: 3