Factors of 3

The factors of 3 are 1 and 3. That is the short answer. But if you want to truly understand what that means, why it works, and how to use it — keep reading. This guide explains everything from scratch, in plain English.

Quick Answer

Factors of 3: 1, 3

Total number of factors: 2

Factor pairs: (1, 3)

Prime factorization: 3

Is 3 a prime number? Yes

What Does "Factor" Actually Mean?

Think about sharing cookies. If you have 3 cookies and you want to share them equally among your friends with none left over — how many ways can you do it?

You could give 1 cookie to each of 3 friends. Or you could give 3 cookies to just 1 friend (lucky them!). Those are the only two options. There is no way to split 3 cookies into groups of 2 because you would have 1 leftover.

That is exactly what factors are. A factor of a number is any number that divides into it perfectly — with nothing left over (no remainder). So the factors of 3 are simply the numbers that 3 can be divided by cleanly.

Simple test to find factors:

3 ÷ 1 = 3  ✓ (no remainder) — so 1 is a factor

3 ÷ 2 = 1.5  ✗ (has a remainder) — so 2 is NOT a factor

3 ÷ 3 = 1  ✓ (no remainder) — so 3 is a factor

All Factors of 3

The complete list of factors of 3 is very short because 3 is a prime number. Here they are:

1
3

That is it. Just two factors. No more, no less. And here is the interesting thing — every single number has 1 and itself as factors. What makes 3 special is that those are the only two it has, which is what makes it a prime number (more on that below).

How to Find the Factors of 3 Step by Step

To find the factors of any number, you start from 1 and work your way up, testing each number to see if it divides evenly. For 3, it looks like this:

Step 1

3 ÷ 1 = 3

1 is a factor

✓
Step 2

3 ÷ 2 = 1 remainder 1

2 is not a factor

✗
Step 3

3 ÷ 3 = 1

3 is a factor — we stop here since we reached the number itself

✓

Once you reach the number itself (3 in this case), you can stop. You will never find a factor larger than the number itself.

Factor Pairs of 3

Factor pairs are two numbers that you multiply together to get the original number. Think of them as multiplication partners. For 3:

1 × 3 = 3

There is only one factor pair for 3. That makes sense because 3 only has two factors (1 and 3), so the only pair you can make is those two together.

Prime Factorization of 3

Prime factorization means breaking a number down into its building blocks — prime numbers only. For 3, this is extremely simple:

3 = 3

3 is already a prime number, so it cannot be broken down further.

Most numbers can be broken into smaller prime factors. For example, 12 = 2 × 2 × 3. But because 3 itself is prime, its prime factorization is just 3. It is already in its simplest form.

Is 3 a Prime Number?

Yes, 3 is a prime number. A prime number is any number that has exactly two factors — 1 and itself. Since the factors of 3 are only 1 and 3, it passes the test perfectly.

3 is actually the second prime number in existence. The first is 2. Here are the first few primes so you can see where 3 fits:

2357111317192329

Notice that 3 is also the only prime number that is divisible by 3 (all multiples of 3 after this are composite because they have 3 as a factor too).

The Divisibility Rule for 3

Here is a really cool trick that math teachers love to share — and once you learn it, you will never forget it. To check if any number is divisible by 3, you add up all its digits. If that sum is divisible by 3, then the whole number is too.

Example 1: Is 27 divisible by 3?

Add the digits: 2 + 7 = 9. Is 9 divisible by 3? Yes (9 ÷ 3 = 3). So 27 is divisible by 3. ✓

Example 2: Is 453 divisible by 3?

Add the digits: 4 + 5 + 3 = 12. Is 12 divisible by 3? Yes (12 ÷ 3 = 4). So 453 is divisible by 3. ✓

Example 3: Is 74 divisible by 3?

Add the digits: 7 + 4 = 11. Is 11 divisible by 3? No. So 74 is not divisible by 3. ✗

This trick works for any number, no matter how large. Try it on 999,999 — add the digits: 9+9+9+9+9+9 = 54, and 54 ÷ 3 = 18. So yes, 999,999 is divisible by 3!

Factors vs. Multiples of 3 — What Is the Difference?

Students often mix these two up. Here is the clearest way to remember the difference:

Factors of 3

Numbers that go INTO 3 evenly. They are smaller than or equal to 3.

1, 3

Multiples of 3

Numbers that 3 goes INTO. They are always bigger than or equal to 3.

3, 6, 9, 12, 15, 18...

An easy way to remember: factors are fewer, multiples are many. Factors shrink or stay the same. Multiples grow forever.

Real-Life Examples Using Factors of 3

Factors are not just a school topic — they show up in everyday life all the time. Here are some simple examples:

🍕

Sharing pizza slices

You have 3 slices of pizza. You can share them between 1 person (3 slices each) or 3 people (1 slice each). Those options come directly from the factors of 3.

📦

Packing items in boxes

If you need to pack 3 toys, you can use 1 big box (3 toys in 1 box) or 3 small boxes (1 toy each). Again — the factors of 3 at work.

📐

Arranging desks in a classroom

A teacher with 3 desks can make 1 row of 3 desks or 3 rows of 1 desk. Those arrangements come from the factor pairs of 3.

Common Mistakes Students Make

Mistake: Forgetting 1 as a factor

1 is a factor of every single number, including 3. Students sometimes only write 3 and forget 1. Both are required.

Mistake: Confusing factors with multiples

A student might write "factors of 3 are 3, 6, 9..." — those are multiples, not factors. Factors of 3 only go up to 3.

Mistake: Thinking 3 is not a factor of itself

Every number is a factor of itself. 3 ÷ 3 = 1 with zero remainder, so 3 is absolutely a factor of 3.

Try It Yourself

Use our free factor calculator to instantly find factors of any number and see its prime factorization tree.

Open Factor Calculator

Frequently Asked Questions

How many factors does 3 have?+
3 has exactly 2 factors: 1 and 3. Because it has exactly two factors, it is classified as a prime number.
What are the factor pairs of 3?+
There is only one factor pair of 3, which is (1, 3). This means 1 × 3 = 3.
Is 3 a composite number?+
No. 3 is not a composite number. Composite numbers have more than two factors. Since 3 has only two factors (1 and 3), it is prime, not composite.
What is the greatest common factor (GCF) of 3 and 6?+
The factors of 3 are 1 and 3. The factors of 6 are 1, 2, 3, and 6. The largest number they share is 3, so GCF(3, 6) = 3.
What is the GCF of 3 and 5?+
The factors of 3 are 1 and 3. The factors of 5 are 1 and 5. The only number they share is 1, so GCF(3, 5) = 1. Numbers with a GCF of 1 are called co-prime.
Is 0 a factor of 3?+
No. You cannot divide by 0 in mathematics. Division by zero is undefined. So 0 is never a factor of any number.
Can a factor of 3 be a negative number?+
In standard school math, we only consider positive factors. Technically -1 × -3 = 3 is valid, but in most grade-level work, factors are treated as positive whole numbers.
Why does 3 only have two factors?+
Because 3 is a prime number. Prime numbers cannot be divided evenly by anything except 1 and themselves. No number between 1 and 3 (just 2) divides into 3 without a remainder.

Summary

  • •The factors of 3 are 1 and 3.
  • •3 has only 2 factors, which makes it a prime number.
  • •The only factor pair is (1, 3).
  • •The prime factorization of 3 is simply 3.
  • •To check if a number is divisible by 3, add its digits — if the sum is divisible by 3, so is the number.
  • •Do not confuse factors (1, 3) with multiples (3, 6, 9, 12...).
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