Factors of 14
14 looks simple at first — just double 7. But it is actually a product of two different prime numbers, which makes it a great number to study. Let us dig into every detail.
Quick Answer
The factors of 14 are: 1, 2, 7, and 14
Total: 4 factors | Type: Composite | Prime factorization: 2 × 7
What is a Factor?
A factor is a whole number that divides into another number exactly — no remainder left over. Think of it like splitting a bag of 14 cookies among friends. If every friend gets the same number of cookies and none are left over, the number of friends is a factor of 14.
Cookie split examples with 14 cookies:
- 1 friend → 14 cookies each → works perfectly ✓
- 2 friends → 7 cookies each → works perfectly ✓
- 3 friends → 4 cookies each + 2 left over → does not work ✕
- 7 friends → 2 cookies each → works perfectly ✓
- 14 friends → 1 cookie each → works perfectly ✓
All Factors of 14
There are exactly 4 factors of 14. Here they are:
1 and 14 are always factors (every number shares these). The interesting ones here are 2 and 7 — both prime numbers.
How to Find the Factors of 14 — Step by Step
The method is straightforward: divide 14 by every whole number from 1 up to 14. If the answer is a whole number with no remainder, that divisor is a factor.
| Division | Result | Remainder | Factor? |
|---|---|---|---|
| 14 ÷ 1 | 14 | 0 | Yes ✓ |
| 14 ÷ 2 | 7 | 0 | Yes ✓ |
| 14 ÷ 3 | 4.67 | 2 | No |
| 14 ÷ 4 | 3.5 | 2 | No |
| 14 ÷ 5 | 2.8 | 4 | No |
| 14 ÷ 6 | 2.33 | 2 | No |
| 14 ÷ 7 | 2 | 0 | Yes ✓ |
| 14 ÷ 8 | 1.75 | 6 | No |
| 14 ÷ 9 | 1.56 | 5 | No |
| 14 ÷ 10 | 1.4 | 4 | No |
| 14 ÷ 11 | 1.27 | 3 | No |
| 14 ÷ 12 | 1.17 | 2 | No |
| 14 ÷ 13 | 1.08 | 1 | No |
| 14 ÷ 14 | 1 | 0 | Yes ✓ |
Pro tip: you only need to check up to √14 ≈ 3.74. Once you pass that point, the remaining factors are just mirror pairs of the ones you already found.
Factor Pairs of 14
A factor pair is two numbers that multiply together to give 14. Every factor has a partner.
Every number pairs with 1 and itself.
14 is even, so 2 always works. Its partner is the prime 7.
Prime Factorization of 14
Prime factorization means breaking a number down into its smallest prime building blocks. Think of it like finding the original ingredients in a recipe.
Step 1: Is 14 divisible by the smallest prime, 2?
14 ÷ 2 = 7 → yes
Step 2: Is 7 divisible by 2?
7 ÷ 2 = 3.5 → no. Try 3: 7 ÷ 3 = 2.33 → no. Try 5: no. Try 7: 7 ÷ 7 = 1 → yes
Step 3: We reached 1. Done.
14 = 2 × 7
Both 2 and 7 are prime. That means 14 is a semiprime — a product of exactly two prime numbers. Numbers like 6 (2 × 3), 10 (2 × 5), 15 (3 × 5), and 21 (3 × 7) are all semiprimes too. They are the simplest composite numbers there are.
14 is a Semiprime
A semiprime is a number that is the product of exactly two prime numbers (which can be the same, like 4 = 2 × 2, or different, like 14 = 2 × 7). Because 2 and 7 are both prime, 14 earns this special label. Here are some semiprimes near 14 for comparison:
| Number | Prime factors | Semiprime? |
|---|---|---|
| 6 | 2 × 3 | Yes ✓ |
| 9 | 3 × 3 | Yes ✓ |
| 10 | 2 × 5 | Yes ✓ |
| 12 | 2² × 3 | No (3 prime factors) |
| 14 | 2 × 7 | Yes ✓ |
| 15 | 3 × 5 | Yes ✓ |
Divisibility Rule for 14
There is no single famous trick for 14, but you can combine the rules for its prime factors 2 and 7:
Rule: A number is divisible by 14 if it is divisible by both 2 and 7.
- Divisible by 2: the last digit must be even (0, 2, 4, 6, or 8)
- Divisible by 7: subtract twice the last digit from the rest; result must be divisible by 7
| Number | Even? | Div by 7? | Div by 14? |
|---|---|---|---|
| 28 | Yes | Yes | Yes ✓ |
| 42 | Yes | Yes | Yes ✓ |
| 56 | Yes | Yes | Yes ✓ |
| 21 | No | Yes | No |
| 16 | Yes | No | No |
Multiples of 14
Multiples are what you get when you multiply 14 by 1, 2, 3... and so on. They are the opposite of factors — instead of going smaller, they grow.
Pattern: every multiple of 14 is even and divisible by 7.
Where Does 14 Show Up in Real Life?
14 appears more often than you might think:
Fortnight
14 days make up one fortnight — a common unit in British English for two weeks.
Valentines Day
February 14 is celebrated worldwide as Valentines Day.
Sonnets
A Shakespeare sonnet has exactly 14 lines — split into three quatrains and a couplet.
Nitrogen
Nitrogen has atomic number 14 on the periodic table.
Rugby
A rugby union team fields 15 players, but a rugby league team fields 13 — the hooker is number 9 and they start with 13 starters, and substitutes go up to 14.
Chess
In the opening of many chess games, 14 half-moves (7 moves per side) is considered early middlegame.
Factors vs Multiples of 14
| Factors of 14 | Multiples of 14 | |
|---|---|---|
| What are they? | Numbers that divide into 14 | Numbers 14 divides into |
| Direction | Smaller than or equal to 14 | Larger than or equal to 14 |
| Count | Exactly 4 | Infinite |
| Examples | 1, 2, 7, 14 | 14, 28, 42, 56... |
14 Compared to Nearby Numbers
| Number | Factors | Count | Type |
|---|---|---|---|
| 12 | 1, 2, 3, 4, 6, 12 | 6 | Composite |
| 13 | 1, 13 | 2 | Prime |
| 14 | 1, 2, 7, 14 | 4 | Composite |
| 15 | 1, 3, 5, 15 | 4 | Composite |
| 16 | 1, 2, 4, 8, 16 | 5 | Composite |
Common Mistakes
✕ Saying 3 is a factor of 14
✓ 14 ÷ 3 = 4 remainder 2. There is a remainder, so 3 is not a factor.
✕ Forgetting that 1 and 14 are factors
✓ 1 and the number itself are always factors of any number.
✕ Confusing factors with multiples
✓ Factors (1, 2, 7, 14) divide into 14. Multiples (14, 28, 42...) are results of multiplying 14.
✕ Thinking 14 is prime because it ends in 4
✓ 14 is composite — it is divisible by 2 and 7. Primes have exactly 2 factors.
Quick Reference Summary
| All factors | 1, 2, 7, 14 |
| Number of factors | 4 |
| Factor pairs | (1, 14) and (2, 7) |
| Prime factorization | 2 × 7 |
| Type | Composite (semiprime) |
| Is perfect square? | No (√14 ≈ 3.742) |
| Is perfect cube? | No |
| Divisibility rule | Divisible by both 2 and 7 |
| Sum of all factors | 1 + 2 + 7 + 14 = 24 |