Module 3 · Number System
Chapter 28: Divisibility Rules
Number System
2 topics
What this chapter covers
The 2 topics below make up Divisibility Rules on the CAT. Click any topic to open its notes, examples and practice test.
Study material & tests
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Formula Reference Sheet
This chapter
Standard rules (single divisors)
| Divisible by 2 / 5 / 10 | Last digit is 0,2,4,6,8 / is 0 or 5 / is 0 |
|---|---|
| Divisible by 3 / 9 | Digit sum is divisible by 3 / by 9 |
| Divisible by 4 / 8 | Last 2 digits ÷ 4 / Last 3 digits ÷ 8 |
| Divisible by 11 | (Sum of odd-place digits − sum of even-place digits) is 0 or a multiple of 11 |
| Divisible by 6 | Divisible by 2 AND by 3 together |
Composite divisors via coprime factors
| Divisible by 12 | Divisible by 3 AND 4 (3, 4 coprime) |
|---|---|
| Divisible by 15 | Divisible by 3 AND 5 |
| Divisible by 18 | Divisible by 2 AND 9 |
| Divisible by 72 | Divisible by 8 AND 9 (NOT 6 × 12 — share a factor) |
| General rule | For n = a × b with HCF(a,b)=1, n | N ⇔ a | N and b | N |
CAT reference
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