Highest Common Factor of 829, 5657 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 829, 5657 i.e. 1 the largest integer that leaves a remainder zero for all numbers.
HCF of 829, 5657 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 829, 5657 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 829, 5657 is 1.
HCF(829, 5657) = 1
HCF of 829, 5657 using Euclid's algorithm
Highest common factor or Highest common divisor (hcd) can be calculated by Euclid's algotithm.
Highest common factor (HCF) of 829, 5657 is 1.
Highest Common Factor of 829,5657 is 1
Step 1: Since 5657 > 829, we apply the division lemma to 5657 and 829, to get
5657 = 829 x 6 + 683
Step 2: Since the reminder 829 ≠ 0, we apply division lemma to 683 and 829, to get
829 = 683 x 1 + 146
Step 3: We consider the new divisor 683 and the new remainder 146, and apply the division lemma to get
683 = 146 x 4 + 99
We consider the new divisor 146 and the new remainder 99,and apply the division lemma to get
146 = 99 x 1 + 47
We consider the new divisor 99 and the new remainder 47,and apply the division lemma to get
99 = 47 x 2 + 5
We consider the new divisor 47 and the new remainder 5,and apply the division lemma to get
47 = 5 x 9 + 2
We consider the new divisor 5 and the new remainder 2,and apply the division lemma to get
5 = 2 x 2 + 1
We consider the new divisor 2 and the new remainder 1,and apply the division lemma 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 829 and 5657 is 1
Notice that 1 = HCF(2,1) = HCF(5,2) = HCF(47,5) = HCF(99,47) = HCF(146,99) = HCF(683,146) = HCF(829,683) = HCF(5657,829) .
HCF using Euclid's Algorithm Calculation Examples
Here are some samples of HCF using Euclid's Algorithm calculations.
Frequently Asked Questions on HCF of 829, 5657 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 829, 5657?
Answer: HCF of 829, 5657 is 1 the largest number that divides all the numbers leaving a remainder zero.
3. How to find HCF of 829, 5657 using Euclid's Algorithm?
Answer: For arbitrary numbers 829, 5657 apply Euclid’s Division Lemma in succession until you obtain a remainder zero. HCF is the remainder in the last but one step.