Factors
Factors of 8
8 is a composite number with four factors. It is also a perfect cube — the only single-digit perfect cube that exists. Let's break it all down, step by step.
Quick Answer
Factors of 8: 1, 2, 4, 8
Factor pairs: (1, 8) and (2, 4) · Prime factorization: 2³
What is a Factor?
A factor is a number that divides into another number exactly — with nothing left over. Think of 8 crayons. Can you split them into equal groups with no leftovers?
- 8 crayons into 1 group of 8 — yes, works perfectly.
- 8 crayons into 2 groups of 4 — yes, works perfectly.
- 8 crayons into 3 groups — 8 ÷ 3 = 2 remainder 2. No.
- 8 crayons into 4 groups of 2 — yes, works perfectly.
- 8 crayons into 5 groups — no. 8 ÷ 5 has a remainder.
- 8 crayons into 6, 7 groups — no remainder in neither case.
- 8 crayons into 8 groups of 1 — yes, works perfectly.
The numbers that worked — 1, 2, 4, and 8 — are the factors of 8.
All Factors of 8
8 ÷ 1 = 8
8 ÷ 2 = 4
8 ÷ 4 = 2
8 ÷ 8 = 1
Total: 4 factors
How to Find the Factors of 8
Divide 8 by every whole number from 1 up to 8. If the remainder is 0, it is a factor.
| Division | Remainder | Factor? |
|---|---|---|
| 8 ÷ 1 = 8 | 0 | Yes |
| 8 ÷ 2 = 4 | 0 | Yes |
| 8 ÷ 3 = 2.67… | 2 | No |
| 8 ÷ 4 = 2 | 0 | Yes |
| 8 ÷ 5 = 1.6 | 3 | No |
| 8 ÷ 6 = 1.33… | 2 | No |
| 8 ÷ 7 = 1.14… | 1 | No |
| 8 ÷ 8 = 1 | 0 | Yes |
Factor Pairs of 8
A factor pair is two numbers that multiply together to give 8. There are exactly two pairs.
Prime Factorization of 8
Prime factorization means breaking a number down to its most basic building blocks — prime numbers only. Think of it like the recipe for making 8.
8 ÷ 2 = 4 (2 is prime — keep it)
4 ÷ 2 = 2 (2 is prime — keep it)
2 ÷ 2 = 1 (2 is prime — keep it, done)
The recipe is 2 × 2 × 2, written as 2³. The only prime building block of 8 is 2 — used three times.
This also makes 8 a power of 2. The sequence goes: 2¹ = 2, 2² = 4, 2³ = 8, 2⁴ = 16... 8 sits right in the middle of that pattern.
8 is a Perfect Cube
A perfect cube is a number you get by multiplying the same integer by itself three times. 8 = 2 × 2 × 2, so the cube root of 8 is exactly 2 — a whole number. That makes 8 the only single-digit perfect cube greater than 1.
∛8 = 2 · 2 × 2 × 2 = 8 · Perfect cube: Yes
√8 ≈ 2.83 · Not a whole number · Perfect square: No
Divisibility Rule for 8
The rule for 8 is a bit more interesting than most: look at the last three digits of a number. If those three digits form a number divisible by 8, the whole number is divisible by 8.
| Number | Last 3 digits | Divisible by 8? |
|---|---|---|
| 1,024 | 024 = 24 | Yes |
| 5,832 | 832 | Yes |
| 3,100 | 100 | No |
| 2,048 | 048 = 48 | Yes |
| 1,234 | 234 | No |
Factors vs Multiples of 8
These two concepts trip up a lot of students. Here is the difference in one sentence: factors go into 8, multiples come out of 8.
| Factors of 8 | Multiples of 8 | |
|---|---|---|
| Direction | Divide into 8 | Multiply out from 8 |
| Examples | 1, 2, 4, 8 | 8, 16, 24, 32… |
| Count | Always finite | Infinite |
8 in the Powers of 2 Sequence
8 is 2³ — the third power of 2. The powers of 2 are everywhere in computers, memory sizes, and binary. Every factor of 8 is also a power of 2:
1
2⁰
2
2¹
4
2²
8
2³
This is rare. Most numbers have factors that are not all powers of the same prime.
Where You See 8 in Real Life
Spider legs
Every spider has exactly 8 legs — a factor of 8 in nature.
Chess board sides
A chessboard is 8 × 8 squares — 64 total, and 8 is a factor of 64.
Bits in a byte
Computers use 8 bits per byte. Storage is always a multiple of 8.
Musical octave
An octave spans 8 notes (do, re, mi, fa, sol, la, ti, do).
Stop sign sides
A stop sign is an octagon — 8 sides. The shape is named after the number.
8-pack snacks
Buns, cans, and juice boxes often come in packs of 8 or 16 (a multiple).
Common Mistakes
Forgetting that 1 and 8 are factors
1 and the number itself are always factors. Never skip them.
Thinking 8 is prime because it sounds small
8 has four factors. Prime numbers have exactly two. 8 is composite.
Confusing 8's factors with its multiples
Factors of 8: 1, 2, 4, 8. Multiples of 8: 8, 16, 24, 32...
Saying the prime factorization is 2 × 4
4 is not prime. You must keep dividing: 2 × 2 × 2 = 2³.
Summary
| All factors | 1, 2, 4, 8 |
| Number of factors | 4 |
| Factor pairs | (1, 8) and (2, 4) |
| Prime factorization | 2³ (= 2 × 2 × 2) |
| Prime or composite | Composite |
| Perfect square | No (√8 ≈ 2.83) |
| Perfect cube | Yes (∛8 = 2) |
| Divisibility rule | Last 3 digits divisible by 8 |