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Factoring in Mathematics

Factoring in Mathematics

• Numbers are positive integers: 1, 2, 3, 4, 5, 6, 7, 8, 9, 10, …
• Even division is division without a remainder or a remainder of “0”.
• The factor of any number is the number that divides that number evenly.
• A prime number is a number that has only two factors, 1 and that number.
• Prime factors are factors that are prime numbers.
• Factoring any number is writing that number in the form product of prime factors (There may be more than 2 factors.)

Factoring

Writing numbers as a product of prime factors And the main prime numbers are 2, 3, 5, 7, 11, 13, 17, and 19 (prime numbers to remember).

Example

1. Find the factors of 24.

Method

Method 1 (DMFT Division)

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

Finding the total number of factors

Finding the total number of factors is the number that divides that number evenly.

(Give prime numbers 2, 3, 5, 7, 11, 13, 17, and 19)

Example

2. Find the factors of 24.

Here’s how to do the factorization of 24:

By factoring 24, we get 2 × 2 × 2 × 3.

= (2 × 2 × 2) × 3

= 8 × 3

= 24

So, show that the factorization of 24 is true.

What are the ways to find all the factors of 24?

By factoring 24 we get 8 × 3.

There are 4 factors of 8: 1, 2, 4, 8.

There are 2 factors of 3: 1, 3.

Therefore, all factors of 24 are 4 × 2 = 8. The numbers are 1, 2, 3, 4, 6, 8, 12, 24.

Finding All Factors of 24 by Factoring Method

Solution By factoring 24, you get 2 × 2 × 2 × 3.

when

Multiply the numbers 2, 4, and 8 by 3 as follows:

2 × 3 = 6

4 × 3 = 12

8 × 3 = 24

(1 is a factor of every number)

Therefore, all factors of 24 are 1, 2, 3, 4, 6, 8, 12, 24.

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

Find the factors of 72.

Here’s how to do factorization of 72:

By factoring 72, we get 2 × 2 × 2 × 3 × 3.

= (2 × 2 × 2) × (3 × 3)

= 8 × 9

= 72

Hence, show that the factorization of 72 is true.

How to find all the factors of 72, how many numbers?

By factoring in 72, we get 8 × 9.

There are 4 factors of 8: 1, 2, 4, 8.

There are 3 factors of 9: 1, 3, 9.

Therefore, all factors of 72 are 4 × 3 = 12 numbers.

when

Multiply the numbers 2, 4, 8 by 3, 9 as follows:

( 2, 4, 8) × 3

2 × 3 = 6

4 × 3 = 12

8 × 3 = 24

( 2, 4, 8) × 9

2 × 9 = 18

4 × 9 = 36

8 × 9 = 72

(1 is a factor of every number)

Therefore, all factors of 72 are 1, 2, 3, 4, 6, 8, 9, 12, 18, 24, 36, 72.

Answer: There are 12 factors of 72: 1, 2, 3, 4, 6, 8, 9, 12, 18, 24, 36, 72.

Check Answer (DMFT, Division)

So the factors of 72 are 1, 2, 3, 4, 6, 8, 9, 12, 18, 24, 36, 72 are true.