Five Properties  Greatest Common Divisor  or  Highest Common Factor

Maths Query 07-12-2024

Do you know?

ARITHMETIC

property 1

GCD of two or more numbers exactly divides the numbers

Example

GCD of 15, 20 = 5 So, the GCD 5 divides both 15 and 20

property 2

GCD of given numbers can't be greater than its numbers

Example

GCD of 8, 14 = 2 So, the GCD 2 is not greater than 8 and 14

property 3

If one number is factor of another number, the smaller number will be its GCD

Example

GCD of 9, 18 = 9 Here, 9 is factor of 18. So, The smaller number 9 is the GCD of 9 and 18

property 4

GCD of co-prime numbers is always 1

Example

GCD of 11, 8 = 1 As GCD is 1 So, 11 and 8 are co-primes

property 5

GCD of consecutive  numbers is always 1

Example

GCD of 21, 22 = 1 21 and 22 are consecutive numbers. So, GCD is 1