Highest Common Factor of 716, 838, 637 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 716, 838, 637 i.e. 1 the largest integer that leaves a remainder zero for all numbers.
HCF of 716, 838, 637 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 716, 838, 637 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 716, 838, 637 is 1.
HCF(716, 838, 637) = 1
HCF of 716, 838, 637 using Euclid's algorithm
Highest common factor or Highest common divisor (hcd) can be calculated by Euclid's algotithm.
Highest common factor (HCF) of 716, 838, 637 is 1.
Highest Common Factor of 716,838,637 is 1
Step 1: Since 838 > 716, we apply the division lemma to 838 and 716, to get
838 = 716 x 1 + 122
Step 2: Since the reminder 716 ≠ 0, we apply division lemma to 122 and 716, to get
716 = 122 x 5 + 106
Step 3: We consider the new divisor 122 and the new remainder 106, and apply the division lemma to get
122 = 106 x 1 + 16
We consider the new divisor 106 and the new remainder 16,and apply the division lemma to get
106 = 16 x 6 + 10
We consider the new divisor 16 and the new remainder 10,and apply the division lemma to get
16 = 10 x 1 + 6
We consider the new divisor 10 and the new remainder 6,and apply the division lemma to get
10 = 6 x 1 + 4
We consider the new divisor 6 and the new remainder 4,and apply the division lemma to get
6 = 4 x 1 + 2
We consider the new divisor 4 and the new remainder 2,and apply the division lemma to get
4 = 2 x 2 + 0
The remainder has now become zero, so our procedure stops. Since the divisor at this stage is 2, the HCF of 716 and 838 is 2
Notice that 2 = HCF(4,2) = HCF(6,4) = HCF(10,6) = HCF(16,10) = HCF(106,16) = HCF(122,106) = HCF(716,122) = HCF(838,716) .
We can take hcf of as 1st numbers and next number as another number to apply in Euclidean lemma
Step 1: Since 637 > 2, we apply the division lemma to 637 and 2, to get
637 = 2 x 318 + 1
Step 2: Since the reminder 2 ≠ 0, we apply division lemma to 1 and 2, to get
2 = 1 x 2 + 0
The remainder has now become zero, so our procedure stops. Since the divisor at this stage is 1, the HCF of 2 and 637 is 1
Notice that 1 = HCF(2,1) = HCF(637,2) .
HCF using Euclid's Algorithm Calculation Examples
Here are some samples of HCF using Euclid's Algorithm calculations.
Frequently Asked Questions on HCF of 716, 838, 637 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 716, 838, 637?
Answer: HCF of 716, 838, 637 is 1 the largest number that divides all the numbers leaving a remainder zero.
3. How to find HCF of 716, 838, 637 using Euclid's Algorithm?
Answer: For arbitrary numbers 716, 838, 637 apply Euclid’s Division Lemma in succession until you obtain a remainder zero. HCF is the remainder in the last but one step.