Divisibility Check (2-20) – Test Number Divisibility

Check if a number is divisible by any integer from 2 to 20 with our free online divisibility checker. Get remainders, divisibility rules, and quick results for all divisors at once.

Number to Check

Understanding Divisibility Rules

Divisibility rules are shortcuts that let you determine if one number divides another without doing the actual division. These mental math tricks have been used for centuries – ancient Greek mathematicians knew many of them. They're especially useful when working with large numbers or when you need a quick answer.

Some rules are obvious (divisible by 2 if the last digit is even). Others are surprisingly clever (divisible by 7 if you double the last digit, subtract from the rest, and the result is divisible by 7). This calculator checks all divisors from 2 to 20 at once and shows which rules apply.

Common Divisibility Rules

Simple Rules (2, 5, 10)

2: Last digit is even (0, 2, 4, 6, 8)

5: Last digit is 0 or 5

10: Last digit is 0

These only require looking at the last digit.

Digit Sum Rules (3, 9)

3: Sum of digits divisible by 3

9: Sum of digits divisible by 9

Add all digits together and check the sum.

Last Digits Rules (4, 8, 16)

4: Last two digits divisible by 4

8: Last three digits divisible by 8

16: Last four digits divisible by 16

Check only the last 2, 3, or 4 digits.

Combined Rules (6, 12, 15, 18)

6: Divisible by both 2 and 3

12: Divisible by both 3 and 4

15: Divisible by both 3 and 5

18: Divisible by both 2 and 9

Check the component prime factors.

Worked Examples

Example 1: Divisibility of 120

Number: 120

Divisible by: 2, 3, 4, 5, 6, 8, 10, 12, 15, 20 (10 divisors)

Not divisible by: 7, 9, 11, 13, 14, 16, 17, 18, 19

120 is highly composite. It's the product 2³ × 3 × 5, giving it many factors.

Example 2: Divisibility of 2520

Number: 2520

Divisible by: 2, 3, 4, 5, 6, 7, 8, 9, 10, 12, 14, 15, 18, 20 (14 divisors!)

Not divisible by: 11, 13, 16, 17, 19

2520 is the smallest number divisible by 1-10. It's the LCM of 1 through 10.

Example 3: Divisibility of 1001

Number: 1001

Divisible by: 7, 11, 13

Not divisible by: 2, 3, 4, 5, 6, 8, 9, 10, 12, 14, 15, 16, 17, 18, 19, 20

1001 = 7 × 11 × 13. This product of three consecutive primes has an interesting pattern.

Example 4: Divisibility of 720

Number: 720 (which is 6!)

Divisible by: 2, 3, 4, 5, 6, 8, 9, 10, 12, 15, 16, 18, 20 (13 divisors)

Not divisible by: 7, 11, 13, 14, 17, 19

720 = 6! = 720. Factorials have many divisors because they're products of all numbers up to n.

Example 5: Divisibility of 999

Number: 999

Divisible by: 3, 9

Not divisible by: 2, 4, 5, 6, 7, 8, 10, 11, 12, 13, 14, 15, 16, 17, 18, 19, 20

999 = 27 × 37 = 3³ × 37. Only divisible by 3 and 9 in our range because it's odd and doesn't end in 0 or 5.

Example 6: Divisibility of 362880

Number: 362880 (which is 9!)

Divisible by: 2, 3, 4, 5, 6, 7, 8, 9, 10, 12, 14, 15, 16, 18, 20 (15 divisors!)

Not divisible by: 11, 13, 17, 19

362880 = 9! is divisible by every number from 1 to 9. Only prime numbers greater than 9 don't divide it.

Quick Fact

2520 is the smallest number divisible by 1 through 10. This highly composite number was known to ancient mathematicians. It's the least common multiple (LCM) of 1, 2, 3, 4, 5, 6, 7, 8, 9, 10. The next such number divisible by 1-12 is 27720. These numbers are useful for creating measurement systems with many convenient subdivisions.

Frequently Asked Questions

Why check divisibility up to 20?

Numbers 2-20 cover the most commonly used divisors in everyday math. They include all single-digit numbers and the most useful two-digit divisors. For larger divisors, you'd typically just do the division.

How does the divisibility by 7 rule work?

Take the last digit, double it, and subtract from the rest of the number. If the result is divisible by 7, so is the original. Example: 343 → 34 - 2(3) = 28, which is divisible by 7.

What does "remainder" mean?

The remainder is what's left after division. If 17 ÷ 5 = 3 remainder 2, it means 5 goes into 17 three times with 2 left over. A remainder of 0 means the number is exactly divisible.

Why is 1 not included in the checks?

Every integer is divisible by 1, so checking would be pointless. We start at 2 because that's the first meaningful divisibility test.

Can I use this for very large numbers?

Yes, but there may be performance limits. JavaScript can safely handle integers up to about 9 quadrillion (9 × 10¹⁵). Beyond that, precision may be lost.

What's a highly composite number?

A highly composite number has more divisors than any smaller positive integer. Examples include 12, 60, 120, 2520, and 5040. These numbers are useful for measurement systems and scheduling.

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