Factors
Factors of 10
Ten is the number we built our entire number system on. We count in groups of ten, our place values run in powers of ten, and ten fingers gave us the decimal system. So what actually divides evenly into 10? Let us work through it carefully.
Quick Answer
The factors of 10 are: 1, 2, 5, 10
Total: 4 factors | Type: Composite | Prime factorization: 2 × 5
What is a factor?
A factor of a number is any whole number that divides into it exactly, leaving no remainder. Think of it like sharing: if you have 10 apples and you can share them equally among a group with nothing left over, that group size is a factor of 10.
You can share 10 apples equally with 1 person, 2 people, 5 people, or 10 people. No other whole number works cleanly. So 1, 2, 5, and 10 are the four factors of 10.
All factors of 10
All four factors of 10 — every whole number that divides 10 with remainder 0.
How to find the factors of 10 (step by step)
The method is simple: try dividing 10 by every whole number from 1 up to 10. If the remainder is 0, that number is a factor.
| Division | Result | Remainder | Factor? |
|---|---|---|---|
| 10 ÷ 1 | 10 | 0 | Yes |
| 10 ÷ 2 | 5 | 0 | Yes |
| 10 ÷ 3 | 3.33... | 1 | No |
| 10 ÷ 4 | 2.5 | 2 | No |
| 10 ÷ 5 | 2 | 0 | Yes |
| 10 ÷ 6 | 1.66... | 4 | No |
| 10 ÷ 7 | 1.42... | 3 | No |
| 10 ÷ 8 | 1.25 | 2 | No |
| 10 ÷ 9 | 1.11... | 1 | No |
| 10 ÷ 10 | 1 | 0 | Yes |
Highlighted rows are the four factors. Four clean divisions, six failed ones.
Factor pairs of 10
A factor pair is two numbers that multiply together to make 10. Think of it as two friends sharing 10 items equally between them.
10 has exactly 2 factor pairs. Since 10 is not a perfect square, no pair uses the same number twice.
Prime factorization of 10
Prime factorization means breaking a number down to its smallest prime building blocks — numbers that cannot be divided further. Think of it as finding the atomic ingredients of 10.
10 ÷ 2 = 5 (2 is prime — keep it)
5 ÷ 5 = 1 (5 is prime — keep it)
We reached 1. Done.
10 = 2 × 5
Unlike 4 (= 2²) or 8 (= 2³) or 9 (= 3²), the number 10 is made from two different primes — 2 and 5. That is exactly why its factors include 1, 2, 5, and 10 but nothing else.
Why 10 is the base of everything
10 is the foundation of the decimal number system (the one we use every day). Every time a digit reaches 10, it rolls over into the next place value. The word "decimal" comes from the Latin decem, meaning ten.
| Power of 10 | Value | Place name |
|---|---|---|
| 10⁰ | 1 | Ones |
| 10¹ | 10 | Tens |
| 10² | 100 | Hundreds |
| 10³ | 1,000 | Thousands |
| 10⁴ | 10,000 | Ten-thousands |
Divisibility rule for 10
The divisibility rule for 10 is the easiest one to remember: a number is divisible by 10 if its last digit is 0. That is it. No adding digits, no doubling, just look at the last digit.
| Number | Last digit | Divisible by 10? |
|---|---|---|
| 30 | 0 | Yes |
| 47 | 7 | No |
| 500 | 0 | Yes |
| 1,234 | 4 | No |
| 7,890 | 0 | Yes |
| 99 | 9 | No |
Where 10 shows up in real life
Your fingers
You have 10 fingers — the original reason humans count in base 10.
A bowling frame
10 pins per frame. A perfect game is 10 frames of 3 strikes = 300 points.
Decimal money
10 pence make a dime-equivalent. Currency is structured in multiples of 10.
Metric system
10 millimetres = 1 centimetre. 10 centimetres = 1 decimetre. All powers of 10.
A sports team lineup
In cricket, 10 wickets per innings. In association football, 10 outfield players.
Roman numeral X
The Roman numeral X represents 10 — used in clocks, centuries (XXI), and Super Bowls.
Factors vs multiples of 10
Factors go into 10. Multiples come out of 10. They move in opposite directions.
| Concept | Definition | Examples |
|---|---|---|
| Factors of 10 | Numbers that divide evenly into 10 | 1, 2, 5, 10 |
| Multiples of 10 | Numbers you get by multiplying 10 | 10, 20, 30, 40... |
How 10 compares to nearby numbers
| Number | Factors | Count | Type |
|---|---|---|---|
| 7 | 1, 7 | 2 | Prime |
| 8 | 1, 2, 4, 8 | 4 | Composite |
| 9 | 1, 3, 9 | 3 | Composite (perfect square) |
| 10 | 1, 2, 5, 10 | 4 | Composite |
| 11 | 1, 11 | 2 | Prime |
| 12 | 1, 2, 3, 4, 6, 12 | 6 | Composite (highly composite) |
Common mistakes students make
✗ Thinking 0 is a factor of 10
✓ Division by zero is undefined. Zero is never a factor of anything.
✗ Forgetting that 1 and 10 are factors
✓ Every number has 1 and itself as factors. They are always included.
✗ Confusing factors with multiples
✓ Factors divide into 10 (they are smaller or equal). Multiples are 10 × something (they are larger).
✗ Saying 10 is prime because it ends in 0
✓ 10 is composite. It has four factors, not two. Ending in 0 actually tells you it is divisible by both 2 and 5.
Quick reference summary
| Number | 10 |
| All factors | 1, 2, 5, 10 |
| Number of factors | 4 |
| Factor pairs | (1, 10) and (2, 5) |
| Prime factorization | 2 × 5 |
| Type | Composite |
| Perfect square? | No |
| Perfect cube? | No |
| Divisibility rule | Last digit must be 0 |