Divisibility and factors — Quantitative aptitude for kids

The method

Rules and powers — “divisibility rules test a number quickly; prime powers count its factors”

1. By 3 or 9: the digit sum divides by 3 or 9. By 4: the last two digits. By 8: the last three digits. By 6: even and divisible by 3. By 11: the sums of alternate digits are equal or differ by 11.
2. Number of factors: write n = p^a × q^b …, then the count is (a + 1) × (b + 1) × ….
3. To make n divisible by d: divide, then add (d − remainder) or take away the remainder.

Use it for: Checking answers, simplifying fractions, divisibility questions in Olympiads and scholarship tests.

Worked example: How many factors does 72 have? → 12

✏️ Practice

Work it out in your head or on paper, type the answer and press Check. Stuck? Press “Show me how”.

🏁 Lesson 3 test

20 questions. Check each answer, then go to the next one. Get 16 or more right to pass.

🏅 Sign in with Google to earn the 🔍 Divisor Detective badge when you pass — and a certificate when you finish all 10 lessons of Part 1 · Number skills. You can still take the test without signing in.

🖨️ Divisibility Rules and Factors Worksheet

• Worksheet set 1 (PDF)
• Worksheet set 2 (PDF)
• Worksheet set 3 (PDF)