Factors of 24 | Prime Factorization of 24 - Explained Simply

Today we are going to present here Factor Tree of 24. The factor is the number that divides the original number. The Factors of 24 are 1, 2, 3, 4, 6, 8, 12 and 24 itself.

What are the factors of 24?

The factors of 24 are all the whole numbers that, when divided into 24, result in a whole number with no remainder. We can also think of them as the whole numbers that multiply together to give 24.

Factor Tree Method of 24: Explained Simply

Steps to find the factors of 24. Start with 1: Every whole number has 1 and itself as factors.

1 × 24 = 24

So, 1 and 24 are factors.

Move to 2: Check if 2 divides 24 evenly.

24 ÷ 2 = 12

So, 2 and 12 are factors.

Move to 3: Check if 3 divides 24 evenly.

24 ÷ 3 = 8

So, 3 and 8 are factors.

Move to 4: Check if 4 divides 24 evenly.

24 ÷ 4 = 6

So, 4 and 6 are factors.

Move to 5: Check if 5 divides 24 evenly.

24 ÷ 5 = 4 with a remainder of 4.

So, 5 is not a factor of 24.

Move to 6: We've already found 6 as a factor (from 4 × 6). Once your "testing number" (e.g., 6) meets or surpasses the "result number" (e.g., the 4 from 4 × 6), you've found all the unique pairs. You can stop.

By following this systematic process, we've identified all the pairs of factors for 24.

Quick Check (Factor Pairs):

1 × 24 = 24
2 × 12 = 24
3 × 8 = 24
4 × 6 = 24

There are a total of 8 factors for the number 24.

Prime Factorization of 24

Prime factorization is a powerful tool that breaks down a number into its prime building blocks. A prime number is a whole number greater than 1 that has only two factors: 1 and itself (examples: 2, 3, 5, 7, 11...).

Steps for prime factorization of 24:

Start dividing by the smallest prime number:

24 ÷ 2 = 12

Continue dividing the result by prime numbers:

12 ÷ 2 = 6

6 ÷ 2 = 3

Stop when you reach a prime number:

3 is a prime number.

So, the prime factorization of 24 is 2 × 2 × 2 × 3. This can also be written as 2^3 \times 3^1.

How to get all factors from prime factors:

Once you have the prime factors, you can combine them in every possible way to find all the factors.

Always include 1: 1 is a factor of every number.

Individual prime factors:

Combinations of two prime factors:

2 × 2 = 4 {2*2}

2 × 3 = 6 {2*3}

Combinations of three prime factors:

2 × 2 × 2 = 8 {2^2}

2 × 2 × 3 = 12 {2^1*3}

Combinations of all prime factors (the number itself):

2 × 2 × 2 × 3 = 24 {2^2*3}

This method ensures you don't miss any factors, especially for larger or more complex numbers.

Listing All the Factors of 24

Combining the results from both methods, we can confidently list all the factors of 24. It's good practice to list them in ascending order for clarity.

The factors of 24 are: 1, 2, 3, 4, 6, 8, 12, 24.