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 768, 972 i.e. 12 the largest integer that leaves a remainder zero for all numbers.
HCF of 768, 972 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 768, 972 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 768, 972 is 12.
HCF(768, 972) = 12
Highest common factor or Highest common divisor (hcd) can be calculated by Euclid's algotithm.
Highest common factor (HCF) of 768, 972 is 12.
Step 1: Since 972 > 768, we apply the division lemma to 972 and 768, to get
972 = 768 x 1 + 204
Step 2: Since the reminder 768 ≠ 0, we apply division lemma to 204 and 768, to get
768 = 204 x 3 + 156
Step 3: We consider the new divisor 204 and the new remainder 156, and apply the division lemma to get
204 = 156 x 1 + 48
We consider the new divisor 156 and the new remainder 48,and apply the division lemma to get
156 = 48 x 3 + 12
We consider the new divisor 48 and the new remainder 12,and apply the division lemma to get
48 = 12 x 4 + 0
The remainder has now become zero, so our procedure stops. Since the divisor at this stage is 12, the HCF of 768 and 972 is 12
Notice that 12 = HCF(48,12) = HCF(156,48) = HCF(204,156) = HCF(768,204) = HCF(972,768) .
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 768, 972?
Answer: HCF of 768, 972 is 12 the largest number that divides all the numbers leaving a remainder zero.
3. How to find HCF of 768, 972 using Euclid's Algorithm?
Answer: For arbitrary numbers 768, 972 apply Euclid’s Division Lemma in succession until you obtain a remainder zero. HCF is the remainder in the last but one step.