Factors of 10 | Prime Factorization of 10 - Explained Simply

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

What are the factors of 10?

We want to find all the whole numbers that can divide 10 without leaving any remainder.

Factor Tree Method of 10: Explained Simply

Let's apply our understanding to the number 10. We can find its factors using a couple of straightforward methods:

Systematic Division Method of 10

This method involves trying to divide 10 by every whole number, starting from 1, and checking for a zero remainder.

Start with 1:

Is 10 divisible by 1? Yes, 10 ÷ 1 = 10 (remainder 0).

1 is a factor of 10.

Try 2:

Is 10 divisible by 2? Yes, 10 ÷ 2 = 5 (remainder 0).

2 is a factor of 10.

Try 3:

Is 10 divisible by 3? No, 10 ÷ 3 = 3 with a remainder of 1.

3 is NOT a factor of 10.

Try 4:

Is 10 divisible by 4? No, 10 ÷ 4 = 2 with a remainder of 2.

4 is NOT a factor of 10.

Try 5:

Is 10 divisible by 5? Yes, 10 ÷ 5 = 2 (remainder 0).

5 is a factor of 10.

Try numbers higher than 5:

You can stop checking once you reach a number that's greater than the result of the division you found earlier (e.g., we found 5 and 2, and 5 is the larger one). Also, you never need to check numbers larger than the number itself.

If we try 6, 7, 8, or 9, none of them will divide 10 evenly.

Finally, try 10:

Is 10 divisible by 10? Yes, 10 ÷ 10 = 1 (remainder 0).

10 is a factor of 10.

Multiplication Pairs of 10

This method involves thinking about which two whole numbers multiply together to give you 10. Factors often come in pairs!

Start with 1:

1 multiplied by what equals 10? 1 × 10 = 10.

Pair: (1, 10)

Move to 2:

2 multiplied by what equals 10? 2 × 5 = 10.

Pair: (2, 5)

Move to 3:

Can 3 be multiplied by a whole number to get 10? No.

Move to 4:

Can 4 be multiplied by a whole number to get 10? No.

Move to 5:

We've already found 5 in a pair (2, 5). Once you start seeing numbers you've already found, you know you've listed all the pairs.

By either method, we arrive at the same set of factors:

The factors of 10 are 1, 2, 5 and 10.

Prime Factorization of 10

There are a couple of common methods for finding the prime factors of a number:

Factor Tree Method: This is a visual way to break down a number into its factors until all branches end in prime numbers.

Division Method: This involves repeatedly dividing the number by the smallest possible prime number until you reach 1.

We'll demonstrate both for the number 10.

Method 1: The Factor Tree

The factor tree is a great visual way to find prime factors.

Start with the number: Write down 10 at the top.

Find two factors: Think of any two numbers that multiply to give you 10 (besides 1 and 10). A good starting point is often the smallest prime number that divides it.

10 can be divided by 2.

10 divided by 2 is 5.

So, draw two branches from 10, labeling them 2 and 5.

/ \

2 5

Check if factors are prime: Look at the numbers at the ends of your branches (2 and 5).

Is 2 a prime number? Yes, its only factors are 1 and 2.

Is 5 a prime number? Yes, its only factors are 1 and 5.

Stop when all branches end in prime numbers: Since both 2 and 5 are prime, we stop. We circle the prime numbers to show they are "finished" branches.

/ \

(2) (5)

Write the prime factorization: The prime factors are the circled numbers.

Prime Factorization of 10 = 2 × 5

Method 2: The Division Method

This method is more systematic and works well for larger numbers too.

Start with the number: Write down 10.

Divide by the smallest prime factor: Find the smallest prime number that can divide 10 evenly. That's 2.

10 ÷ 2 = 5

Write the prime factor (2) on the left and the result (5) below.

2 | 10

Continue dividing the result: Now, take the new number (5) and find the smallest prime number that can divide it evenly.

The smallest prime number that divides 5 is 5 itself.

5 ÷ 5 = 1

Write the prime factor (5) on the left and the result (1) below.

2 | 10

5 | 5

Stop when you reach 1: When the result is 1, you're done.

Collect the prime factors: The prime factors are all the numbers you divided by on the left side.

Prime Factorization of 10 = 2 × 5

Conclusion

Whether you use a factor tree or the division method, the result for 10 is the same: its prime factorization is 2 × 5. This means that the number 10 is uniquely built from the prime numbers 2 and 5 multiplied together.