Yes. A prime has exactly two factors, 1 and itself, and 2 fits that rule. It is the smallest prime number.

What is the prime factorization of 2?

The prime factorization of 2 is just 2, because 2 is already prime and cannot be split any further.

Factors of 2 - The Only Even Prime Number

Q: What are the factors of 2?

The factors of 2 are 1 and 2. Those are the only two whole numbers that divide 2 with no remainder.

Q: Why is 2 the only even prime?

Every even number is divisible by 2. So any even number bigger than 2 has at least three factors (1, 2 and itself), which makes it composite.

What Are the Factors of 2?

Hand two cookies to two friends and the split is clean: one each. Hand them to three friends and someone is left out. That tiny test is what a factor is all about. A factor is a whole number that divides another number exactly, with nothing left over.

The factors of 2 are 1 and 2. Nothing else fits, because any number bigger than 2 is too large to go into it, and 2 cannot be shared evenly by anything between them.

The Only Factor Pair of 2

Pairs are the quickest way to hunt for factors. You look for two numbers that multiply to your target. For 2 there is just one pair.

Handwritten notebook page titled Factors of 2 showing 1 × 2 = 2, with the two factors 1 and 2 circled in red and the note 2 factors — Factors of 2: the single pair 1 × 2, with both factors circled.

Start with 1 × 2 = 2. Every number has this pair.
Try 2. It is already in your pair, so you have met in the middle.
Stop. There is nothing else to test, so the list is 1 and 2.

Why 2 Is Prime: A Quick Proof

A prime number has exactly two factors: 1 and itself. Two fits perfectly. It is the smallest prime number, and the first one you meet when counting.

Handwritten page with the number 2 circled in red, then 2 ÷ 1 = 2 and 2 ÷ 2 = 1 in blue, and the green note 2 is prime, only 1 and 2 divide it — Dividing 2 by 1 and by 2 works. Nothing else does, so 2 is prime.

Because 2 is already prime, its factor tree has no branches at all. The prime factorization of 2 is simply 2.

The only even prime

Here is the fact that makes 2 famous. Every even number can be divided by 2. So any even number bigger than 2 has at least three factors: 1, 2 and itself. That rules it out as prime. This leaves 2 as the only even prime number, and every other prime is odd.

Where You Use the Factors of 2 Every Day

Even or odd? A number is even when 2 is one of its factors. That is the whole definition.
Halving. Cutting a pizza, a bill or a rope in half is dividing by 2.
Binary. Computers count with just two digits, and every value is built from powers of 2.

Common Factors of 2 With Other Numbers

The greatest common factor (GCF) of 2 and any even number is 2, and with any odd number it is 1. For 2 and 6, the shared factors are 1 and 2, so the GCF is 2. That lets you simplify 2/6 by dividing top and bottom by 2 to get 1/3.

Quick Practice

Is 2 a factor of 14? Yes, because 14 ÷ 2 = 7 with nothing left. Is it a factor of 15? No, because 15 ÷ 2 leaves 1. Try a few more numbers and check them with the calculator.

Factors of 2