Highest Common Factor of 622, 972 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 622, 972 i.e. 2 the largest integer that leaves a remainder zero for all numbers.
HCF of 622, 972 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 622, 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 622, 972 is 2.
HCF(622, 972) = 2
HCF of 622, 972 using Euclid's algorithm
Highest common factor or Highest common divisor (hcd) can be calculated by Euclid's algotithm.
Highest common factor (HCF) of 622, 972 is 2.
Highest Common Factor of 622,972 is 2
Step 1: Since 972 > 622, we apply the division lemma to 972 and 622, to get
972 = 622 x 1 + 350
Step 2: Since the reminder 622 ≠ 0, we apply division lemma to 350 and 622, to get
622 = 350 x 1 + 272
Step 3: We consider the new divisor 350 and the new remainder 272, and apply the division lemma to get
350 = 272 x 1 + 78
We consider the new divisor 272 and the new remainder 78,and apply the division lemma to get
272 = 78 x 3 + 38
We consider the new divisor 78 and the new remainder 38,and apply the division lemma to get
78 = 38 x 2 + 2
We consider the new divisor 38 and the new remainder 2,and apply the division lemma to get
38 = 2 x 19 + 0
The remainder has now become zero, so our procedure stops. Since the divisor at this stage is 2, the HCF of 622 and 972 is 2
Notice that 2 = HCF(38,2) = HCF(78,38) = HCF(272,78) = HCF(350,272) = HCF(622,350) = HCF(972,622) .
HCF using Euclid's Algorithm Calculation Examples
Here are some samples of HCF using Euclid's Algorithm calculations.
Frequently Asked Questions on HCF of 622, 972 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 622, 972?
Answer: HCF of 622, 972 is 2 the largest number that divides all the numbers leaving a remainder zero.
3. How to find HCF of 622, 972 using Euclid's Algorithm?
Answer: For arbitrary numbers 622, 972 apply Euclid’s Division Lemma in succession until you obtain a remainder zero. HCF is the remainder in the last but one step.
