Highest Common Factor of 612, 721 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 612, 721 i.e. 1 the largest integer that leaves a remainder zero for all numbers.
HCF of 612, 721 is 1 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 612, 721 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 612, 721 is 1.
HCF(612, 721) = 1
HCF of 612, 721 using Euclid's algorithm
Highest common factor or Highest common divisor (hcd) can be calculated by Euclid's algotithm.
Highest common factor (HCF) of 612, 721 is 1.
Highest Common Factor of 612,721 is 1
Step 1: Since 721 > 612, we apply the division lemma to 721 and 612, to get
721 = 612 x 1 + 109
Step 2: Since the reminder 612 ≠ 0, we apply division lemma to 109 and 612, to get
612 = 109 x 5 + 67
Step 3: We consider the new divisor 109 and the new remainder 67, and apply the division lemma to get
109 = 67 x 1 + 42
We consider the new divisor 67 and the new remainder 42,and apply the division lemma to get
67 = 42 x 1 + 25
We consider the new divisor 42 and the new remainder 25,and apply the division lemma to get
42 = 25 x 1 + 17
We consider the new divisor 25 and the new remainder 17,and apply the division lemma to get
25 = 17 x 1 + 8
We consider the new divisor 17 and the new remainder 8,and apply the division lemma to get
17 = 8 x 2 + 1
We consider the new divisor 8 and the new remainder 1,and apply the division lemma to get
8 = 1 x 8 + 0
The remainder has now become zero, so our procedure stops. Since the divisor at this stage is 1, the HCF of 612 and 721 is 1
Notice that 1 = HCF(8,1) = HCF(17,8) = HCF(25,17) = HCF(42,25) = HCF(67,42) = HCF(109,67) = HCF(612,109) = HCF(721,612) .
HCF using Euclid's Algorithm Calculation Examples
Here are some samples of HCF using Euclid's Algorithm calculations.
Frequently Asked Questions on HCF of 612, 721 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 612, 721?
Answer: HCF of 612, 721 is 1 the largest number that divides all the numbers leaving a remainder zero.
3. How to find HCF of 612, 721 using Euclid's Algorithm?
Answer: For arbitrary numbers 612, 721 apply Euclid’s Division Lemma in succession until you obtain a remainder zero. HCF is the remainder in the last but one step.