HCF

Highest Common Factor (HCF): HCF of two or more given numbers is the greatest number that divides each of them exactly. Thus 7 is the HCF of 14 and 21.

HCF is also called Highest Common Divisor or Greatest Common Divisor.

Methods to find HCF

Method of prime factors: Break the given numbers into prime factors and then find the product of the prime factors common to all the numbers. This product will be the required HCF.

Example: HCF of 25, 30 and 55 is

25 = 5 x 5

30 = 2 x 3 x 5

55 = 5 x 11

The factor common to all the numbers is 5, hence 5 is the HCF.

Method of Division: Divide the greater number by the smaller number. if there is remainder then divide the divisor by the remainder. if again there is remainder, then again divide the divisor by the next remainder and so on until no remainder is left. The last remainder is the required HCF.

Example: HCF of 61 and 187 is

Thus HCF is 17.

HCF of decimals

First find the HCF of the given numbers without decimals and then put the decimal in the result after the number of digits which is equal to the maximum digits after the decimal in the given numbers from right to left.

Example: What is the HCF of 1.1, 6.93 and 0.0572?

HCF of 11, 893 and 572 is 11

Required HCF is 0.0011 ( since maximum decimal places is 4 in 0.0572)