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Introduction to HCF and LCM.

• Factors: Each of the number is multiplied together to form a product is called factor of the product. In other words, a factor of given number divides the given number exatly.

Example:

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

= 1, 2, 3, 4, 6, 8, 12 and 24 are the factors of 24.

• Common factors: A common factor of two or more number is a number which divides each of the given number exactly.

Example:

Fctors of 6 = 1, 2, 3 and 6 and factors of 8 = 1, 2, 4 and 8.

Common factors of 6 and 8 = 1 and 2.
Note: It can easily be shown that each common facotr(1 and 2) divides the given numbers 6 and 8 exactly.

• Prime Factor: It is the factor of a given number which is a prime number.

Example:

Factor of 14 = 1, 2, 7 aand 14.
Out of these 2 and 7 are prime numbers.
Therefore, 2 and 7 are prime factors of 4.

• Repeated prime factors: A number can have two or more different repeated prime factors.

Example:

since, 8 = 2 x 2 x 2; 2 is said to be repeated prime factor of 8.