Highest Common Factor of 821, 9610 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 821, 9610 i.e. 1 the largest integer that leaves a remainder zero for all numbers.
HCF of 821, 9610 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 821, 9610 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 821, 9610 is 1.
HCF(821, 9610) = 1
HCF of 821, 9610 using Euclid's algorithm
Highest common factor or Highest common divisor (hcd) can be calculated by Euclid's algotithm.
Highest common factor (HCF) of 821, 9610 is 1.
Highest Common Factor of 821,9610 is 1
Step 1: Since 9610 > 821, we apply the division lemma to 9610 and 821, to get
9610 = 821 x 11 + 579
Step 2: Since the reminder 821 ≠ 0, we apply division lemma to 579 and 821, to get
821 = 579 x 1 + 242
Step 3: We consider the new divisor 579 and the new remainder 242, and apply the division lemma to get
579 = 242 x 2 + 95
We consider the new divisor 242 and the new remainder 95,and apply the division lemma to get
242 = 95 x 2 + 52
We consider the new divisor 95 and the new remainder 52,and apply the division lemma to get
95 = 52 x 1 + 43
We consider the new divisor 52 and the new remainder 43,and apply the division lemma to get
52 = 43 x 1 + 9
We consider the new divisor 43 and the new remainder 9,and apply the division lemma to get
43 = 9 x 4 + 7
We consider the new divisor 9 and the new remainder 7,and apply the division lemma to get
9 = 7 x 1 + 2
We consider the new divisor 7 and the new remainder 2,and apply the division lemma to get
7 = 2 x 3 + 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 821 and 9610 is 1
Notice that 1 = HCF(2,1) = HCF(7,2) = HCF(9,7) = HCF(43,9) = HCF(52,43) = HCF(95,52) = HCF(242,95) = HCF(579,242) = HCF(821,579) = HCF(9610,821) .
HCF using Euclid's Algorithm Calculation Examples
Here are some samples of HCF using Euclid's Algorithm calculations.
Frequently Asked Questions on HCF of 821, 9610 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 821, 9610?
Answer: HCF of 821, 9610 is 1 the largest number that divides all the numbers leaving a remainder zero.
3. How to find HCF of 821, 9610 using Euclid's Algorithm?
Answer: For arbitrary numbers 821, 9610 apply Euclid’s Division Lemma in succession until you obtain a remainder zero. HCF is the remainder in the last but one step.