Highest Common Factor of 2506, 657 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 2506, 657 i.e. 1 the largest integer that leaves a remainder zero for all numbers.
HCF of 2506, 657 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 2506, 657 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 2506, 657 is 1.
HCF(2506, 657) = 1
HCF of 2506, 657 using Euclid's algorithm
Highest common factor or Highest common divisor (hcd) can be calculated by Euclid's algotithm.
Highest common factor (HCF) of 2506, 657 is 1.
Highest Common Factor of 2506,657 is 1
Step 1: Since 2506 > 657, we apply the division lemma to 2506 and 657, to get
2506 = 657 x 3 + 535
Step 2: Since the reminder 657 ≠ 0, we apply division lemma to 535 and 657, to get
657 = 535 x 1 + 122
Step 3: We consider the new divisor 535 and the new remainder 122, and apply the division lemma to get
535 = 122 x 4 + 47
We consider the new divisor 122 and the new remainder 47,and apply the division lemma to get
122 = 47 x 2 + 28
We consider the new divisor 47 and the new remainder 28,and apply the division lemma to get
47 = 28 x 1 + 19
We consider the new divisor 28 and the new remainder 19,and apply the division lemma to get
28 = 19 x 1 + 9
We consider the new divisor 19 and the new remainder 9,and apply the division lemma to get
19 = 9 x 2 + 1
We consider the new divisor 9 and the new remainder 1,and apply the division lemma to get
9 = 1 x 9 + 0
The remainder has now become zero, so our procedure stops. Since the divisor at this stage is 1, the HCF of 2506 and 657 is 1
Notice that 1 = HCF(9,1) = HCF(19,9) = HCF(28,19) = HCF(47,28) = HCF(122,47) = HCF(535,122) = HCF(657,535) = HCF(2506,657) .
HCF using Euclid's Algorithm Calculation Examples
Here are some samples of HCF using Euclid's Algorithm calculations.
Frequently Asked Questions on HCF of 2506, 657 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 2506, 657?
Answer: HCF of 2506, 657 is 1 the largest number that divides all the numbers leaving a remainder zero.
3. How to find HCF of 2506, 657 using Euclid's Algorithm?
Answer: For arbitrary numbers 2506, 657 apply Euclid’s Division Lemma in succession until you obtain a remainder zero. HCF is the remainder in the last but one step.