Factors of 20 | Prime Factorization of 20 - Explained Simply

Today we are going to present here Factor Tree of 20. The factor is the number that divides the original number. The factors of 20 are 1, 2, 4, 5, 10 and 20 itself.

What are the factors of 20?

The factors of 20 are all the whole numbers that, when divided into 20, result in a whole number with no remainder. We can also think of them as the whole numbers that multiply together to give 20.

Factor Tree Method of 20: Explained Simply

Let's find the factors of 20 step-by-step:

Start with 1:

1 divides 20 evenly (20 ÷ 1 = 20).

So, 1 and 20 are factors.

Try 2:

2 divides 20 evenly (20 ÷ 2 = 10).

So, 2 and 10 are factors.

Try 3:

3 does not divide 20 evenly (20 ÷ 3 = 6 with a remainder of 2).

So, 3 is not a factor.

Try 4:

4 divides 20 evenly (20 ÷ 4 = 5).

So, 4 and 5 are factors.

Try 5:

We've already found 5 as a factor in the previous step (paired with 4). This indicates we've found all unique factor pairs. We don't need to check numbers beyond 4, as we would only find factors we've already listed as partners. (The square root of 20 is approximately 4.47, so we only need to check numbers up to 4).

Listing the Factors of 20

Based on our systematic search, the factors of 20, listed in ascending order, are: 1, 2, 4, 5, 10, 20.

Pair Factors of 20

We can also visualize them in their factor pairs:

1 × 20 = 20 (1, 20)
2 × 10 = 20 (2, 10)
4 × 5 = 20 (4, 5)
5 × 4 = 20 (5, 4)
10 × 2 = 20 (10, 2)
20 × 1 = 20 (20, 1)

Prime Factorization of 20

Now that we understand the ingredients, let's find the prime factors of 20 using two common and easy-to-follow methods.

The Division Method of 20 (Successive Division)

This method involves repeatedly dividing the number by the smallest possible prime number until you can't divide it anymore, then moving to the next prime number.

Start with 20:

Is 20 divisible by the smallest prime number, 2?

Yes! 20 ÷ 2 = 10.

Our first prime factor is 2.

Now look at the result, 10. Is 10 divisible by 2?

Yes! 10 ÷ 2 = 5.

Our second prime factor is 2.

Now look at the result, 5. Is 5 divisible by 2?

No (it would leave a remainder).

Try the next smallest prime number, 3:

Is 5 divisible by 3? No.

Try the next smallest prime number, 5:

Is 5 divisible by 5? Yes! 5 ÷ 5 = 1.

Our third prime factor is 5.

Stop when your final result is 1.

The prime numbers we used to divide are our prime factors 2, 2 and 5.

So, 20 can be written as a product of its prime factors: 2 × 2 × 5.

The Factor Tree of 20

The factor tree method is a visual way to break down a number into its prime factors.

Start with 20 at the top.

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Find any two factors of 20 (besides 1 and 20). For example, 2 and 10. Draw branches to them.

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2 10

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Check if these factors are prime.

2 is a prime number, so we circle it. We can't break it down further.

10 is not prime (it's composite), so we need to break it down further.

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(2) 10

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If we break down 10 into two of its factors, we get 2 and 5. To see more details, check the factors of 10 with step-by-step explanation.

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(2) 10

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2 5

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Check if these new factors are prime.

2 is a prime number, so we circle it.

5 is a prime number, so we circle it.

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(2) 10

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(2) (5)

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All the numbers at the ends of the branches are now circled prime numbers. These are the prime factors of 20.

The prime factors collected from the bottom of the tree are 2, 2 and 5.

Again, 20 can be written as: 2 × 2 × 5.

Based on both methods, we arrive at the same conclusion:

The prime factorization of 20 is 2 × 2 × 5 (2*2*5).

When we list the distinct prime factors of 20, they are 2 and 5.

We can also write this in a more compact way using exponents: 2² × 5.

(Because 2 appears twice, it's 2 to the power of 2, or 2 squared).