What Are the Factors of 6?
Think of a six-pack of juice. You can carry it as 1 row of 6 or 2 rows of 3, and you could also split it into 3 bundles of 2. Each of those neat arrangements is a factor. A factor is a whole number that divides another number exactly, with nothing left over.
The factors of 6 are 1, 2, 3 and 6. That is four numbers, and 6 has a special secret that most numbers do not.
Factor Pairs of 6
The fastest method is to hunt for pairs that multiply to 6, starting from the outside.
- Start with 1 × 6. Every number has this pair.
- Try 2. Since 6 ÷ 2 = 3, write 2 × 3.
- Try 3. It is already in your list, so you have met in the middle and you are done.
Prime Factorization of 6
Prime factors tell you what a number is built from. Six splits into 2 and 3, and both are already prime, so the tree has only one split.
So 6 = 2 × 3. Two different primes, each used once. Using the shortcut, (1 + 1) × (1 + 1) = 4 factors, which matches the list.
Why 6 Is a Perfect Number
Add up every factor of 6 except 6 itself: 1 + 2 + 3 = 6. The factors add right back to the number. Mathematicians call a number like this a perfect number, and 6 is the smallest one. The next is 28.
Is 6 prime or composite?
Composite. A prime has only two factors, but 6 has four. The sum of all four factors is 12, which is exactly double 6, another way of spotting a perfect number.
Real-Life Uses of the Factors of 6
- Six-packs and egg trays can be shared fairly between 2 or 3 people, or laid out in tidy rows.
- Dice have 6 faces, and a hexagon has 6 equal sides.
- Half and third. Because 2 and 3 are both factors, 6 splits cleanly into halves and thirds.
Common Factors of 6 With Other Numbers
The factors of 9 are 1, 3 and 9, so 6 and 9 share 1 and 3, and the GCF is 3. That simplifies 6/9 to 2/3 after dividing the top and bottom by 3.
Quick Practice
Which of these are factors of 6: 3, 4 or 6? That is 3 and 6, since 6 ÷ 4 leaves 2. Try 12 next and check your list with the calculator.