Created By : Jatin Gogia
Reviewed By : Rajasekhar Valipishetty
Last Updated : Apr 06, 2023
HCF Calculator using the Euclid Division Algorithm helps you to find the Highest common factor (HCF) easily for 324, 972, 156 i.e. 12 the largest integer that leaves a remainder zero for all numbers.
HCF of 324, 972, 156 is 12 the largest number which exactly divides all the numbers i.e. where the remainder is zero. Let us get into the working of this example.
Consider we have numbers 324, 972, 156 and we need to find the HCF of these numbers. To do so, we need to choose the largest integer first and then as per Euclid's Division Lemma a = bq + r where 0 ≤ r ≤ b
Highest common factor (HCF) of 324, 972, 156 is 12.
HCF(324, 972, 156) = 12
Highest common factor or Highest common divisor (hcd) can be calculated by Euclid's algotithm.
Highest common factor (HCF) of 324, 972, 156 is 12.
Step 1: Since 972 > 324, we apply the division lemma to 972 and 324, to get
972 = 324 x 3 + 0
The remainder has now become zero, so our procedure stops. Since the divisor at this stage is 324, the HCF of 324 and 972 is 324
Notice that 324 = HCF(972,324) .
We can take hcf of as 1st numbers and next number as another number to apply in Euclidean lemma
Step 1: Since 324 > 156, we apply the division lemma to 324 and 156, to get
324 = 156 x 2 + 12
Step 2: Since the reminder 156 ≠ 0, we apply division lemma to 12 and 156, to get
156 = 12 x 13 + 0
The remainder has now become zero, so our procedure stops. Since the divisor at this stage is 12, the HCF of 324 and 156 is 12
Notice that 12 = HCF(156,12) = HCF(324,156) .
Here are some samples of HCF using Euclid's Algorithm calculations.
1. What is the Euclid division algorithm?
Answer: Euclid's Division Algorithm is a technique to compute the Highest Common Factor (HCF) of given positive integers.
2. what is the HCF of 324, 972, 156?
Answer: HCF of 324, 972, 156 is 12 the largest number that divides all the numbers leaving a remainder zero.
3. How to find HCF of 324, 972, 156 using Euclid's Algorithm?
Answer: For arbitrary numbers 324, 972, 156 apply Euclid’s Division Lemma in succession until you obtain a remainder zero. HCF is the remainder in the last but one step.