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What are factors in maths

Factors of a given number are numbers that when multiplied together give us the original number. For example, the number 12 can be obtained by multiplying the following numbers:

1 and 12
2 and 6
3 and 4

Thus 1, 2, 3, 4, 6, and 12 are the factors of the number 12.

A number can have many factors.

Factors are whole numbers that can be either composite numbers or prime factors.

Composite numbers are natural numbers other than prime numbers.

A prime number is not divisible by any number other than 1 and the number itself. Thus, prime numbers have only two factors - the number 1 and the number itself.

Practice questions

Question: Find the factors of the number 21.
( Answer: Factors of 21 are 1, 3, 7, 21 )
Question: Find the factors of the number 17.
( Answer: Factors of 17 are 1, 17 . Note: 17 is a prime number )
Question: Find the factors of the number 64.
( Answer: Factors of 64 are 1, 2, 4, 8, 16, 32, 64 )

Common factors

Factors that are common to two or more numbers are known as common factors. For example, consider the number 12 and 18.
Factors of 12: 1, 2, 3, 4, 6, 12
Factors of 18: 1, 2, 3, 6, 9, 18

The number 1, 2, 3, 6 are the common factors of 12 and 18

Practice questions
Question: Find the common factors of 10 and 30.
( Answer:     Factors of 10 = 1, 2, 5, 10
Factors of 30 = 1, 2, 3, 5, 6, 10, 15, 30
Common factors of 10 and 30 are: 1, 2, 5, 10
)
Question: Find the common factors of 24 and 64.
( Answer:     Factors of 24 = 1, 2, 3, 4, 6, 8, 12, 24
Factors of 64 = 1, 2, 4, 8, 16, 32, 64
Common factors of 24 and 64 are: 1, 2, 4, 8
)
Question: Find the common factors of 18 and 24 and 99.
( Answer:     Factors of 18 = 1, 2, 3, 6, 9, 18
Factors of 24 = 1, 2, 3, 4, 6, 8, 12, 24
Factors of 99 = 1, 3, 9, 11, 33, 99
Common factors of 18, 24 and 99 are: 1, 3
)

Prime factorization

In this method, we try to find the prime numbers which multiply together to make the original number.

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