Number System
8 questions · EasyMediumHard
Number system covers remainders, factors, divisibility and the properties of numbers. Many questions ask for the smallest number to add or subtract to make something divisible.
💡 Quick tricks
- To make n divisible by d, add d − (n mod d), or subtract n mod d.
- If n = p^a × q^b × …, n has (a + 1)(b + 1)… divisors.
- Remainders can be added and multiplied, then reduced again at the end.
🎯 Try it yourself
Tap an answer. You'll see if it's right, and why. Easy ones come first.
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Q1Easy
Smallest number to add to 1,338 to make it divisible by 12?
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Answer: C. 6
💡 1,338 ÷ 12 leaves remainder 6, so add 12 − 6 = 6.
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Q2Easy
Smallest number to add to 1,215 to make it divisible by 12?
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Answer: A. 9
💡 1,215 ÷ 12 leaves remainder 3, so add 12 − 3 = 9.
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Q3Easy
Smallest number to add to 876 to make it divisible by 10?
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Answer: C. 4
💡 876 ÷ 10 leaves remainder 6, so add 10 − 6 = 4.
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Q4Medium
What is the unit digit of 17^52?
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Answer: C. 1
💡 Unit digits of powers of 7 repeat in a cycle; for the power 52 the unit digit is 1.
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Q5Medium
What is the unit digit of 64^66?
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Answer: D. 6
💡 Unit digits of powers of 4 repeat in a cycle; for the power 66 the unit digit is 6.
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Q6Medium
What is the unit digit of 29^18?
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Answer: C. 1
💡 Unit digits of powers of 9 repeat in a cycle; for the power 18 the unit digit is 1.
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Q7Hard
How many factors does 216 have?
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Answer: A. 16
💡 216 = 2^3 × 3^3 × 5^0, so it has (3+1)(3+1)(0+1) = 16 divisors.
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Q8Hard
How many factors does 50 have?
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Answer: C. 6
💡 50 = 2^1 × 3^0 × 5^2, so it has (1+1)(0+1)(2+1) = 6 divisors.
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