Highest Common Factor of 422, 756 using Euclid's algorithm
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 422, 756 i.e. 2 the largest integer that leaves a remainder zero for all numbers.
HCF of 422, 756 is 2 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 422, 756 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 422, 756 is 2.
HCF(422, 756) = 2
HCF of 422, 756 using Euclid's algorithm
Highest common factor or Highest common divisor (hcd) can be calculated by Euclid's algotithm.
Highest common factor (HCF) of 422, 756 is 2.
Highest Common Factor of 422,756 is 2
Step 1: Since 756 > 422, we apply the division lemma to 756 and 422, to get
756 = 422 x 1 + 334
Step 2: Since the reminder 422 ≠ 0, we apply division lemma to 334 and 422, to get
422 = 334 x 1 + 88
Step 3: We consider the new divisor 334 and the new remainder 88, and apply the division lemma to get
334 = 88 x 3 + 70
We consider the new divisor 88 and the new remainder 70,and apply the division lemma to get
88 = 70 x 1 + 18
We consider the new divisor 70 and the new remainder 18,and apply the division lemma to get
70 = 18 x 3 + 16
We consider the new divisor 18 and the new remainder 16,and apply the division lemma to get
18 = 16 x 1 + 2
We consider the new divisor 16 and the new remainder 2,and apply the division lemma to get
16 = 2 x 8 + 0
The remainder has now become zero, so our procedure stops. Since the divisor at this stage is 2, the HCF of 422 and 756 is 2
Notice that 2 = HCF(16,2) = HCF(18,16) = HCF(70,18) = HCF(88,70) = HCF(334,88) = HCF(422,334) = HCF(756,422) .
HCF using Euclid's Algorithm Calculation Examples
Here are some samples of HCF using Euclid's Algorithm calculations.
Frequently Asked Questions on HCF of 422, 756 using Euclid's Algorithm
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 422, 756?
Answer: HCF of 422, 756 is 2 the largest number that divides all the numbers leaving a remainder zero.
3. How to find HCF of 422, 756 using Euclid's Algorithm?
Answer: For arbitrary numbers 422, 756 apply Euclid’s Division Lemma in succession until you obtain a remainder zero. HCF is the remainder in the last but one step.