CLASS-4
H.C.F - PRIME FACTORIZATION METHOD
Finding H.C.F Via Prime Factorization Method -
HCF
1. PRIME FACTORIZATION METHOD : In this method
§ STEP 1.) First we find the prime factors of the given numbers separately by factorization.
§ STEP 2.) Then we underline the common prime factors of the numbers and write it down.
§ STEP 3.) We multiply the common prime factors
§ STEP 4.) The product of these common prime factors is the H.C.F of the given numbers.
SOLVED EXAMPLE:
Q. Find the HCF using PRIME FACTORIZATION METHOD.
210, 360, 150
Ans.)
STEP 1.) Write the Prime Factors and do the red color the Common Factors
210 = 2 x 3 x 5 x 7 x 1
360 = 2 x 2 x 2 x 3 x 3 x 5 x 1
150 = 2 x 3 x 5 x 5 x 1
STEP 2.)
Common factors = 2 x 3 x 5 x 1 (Multiply the Common Factors)
STEP 3.)
H.C.F = 30 (The product is the H.C.F)
STEP 4.)
Answer: The HCF of 210, 360 and 150 is 30. (Ans.)
Important Note -
Two numbers are called Co-prime if their HCF is 1.
Example: 12 and 25
Factors of 12 are 1, 2, 3, 4, 6 and 12.
Factors of 25 are 1, 5 and 25. Common Factor is 1
∴ HCF is 1
So, 12 and 25 are Co-prime.