Highest Common Factor of 8962, 6813, 22710 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 8962, 6813, 22710 i.e. 1 the largest integer that leaves a remainder zero for all numbers.
HCF of 8962, 6813, 22710 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 8962, 6813, 22710 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 8962, 6813, 22710 is 1.
HCF(8962, 6813, 22710) = 1
HCF of 8962, 6813, 22710 using Euclid's algorithm
Highest common factor or Highest common divisor (hcd) can be calculated by Euclid's algotithm.
Highest common factor (HCF) of 8962, 6813, 22710 is 1.
Highest Common Factor of 8962,6813,22710 is 1
Step 1: Since 8962 > 6813, we apply the division lemma to 8962 and 6813, to get
8962 = 6813 x 1 + 2149
Step 2: Since the reminder 6813 ≠ 0, we apply division lemma to 2149 and 6813, to get
6813 = 2149 x 3 + 366
Step 3: We consider the new divisor 2149 and the new remainder 366, and apply the division lemma to get
2149 = 366 x 5 + 319
We consider the new divisor 366 and the new remainder 319,and apply the division lemma to get
366 = 319 x 1 + 47
We consider the new divisor 319 and the new remainder 47,and apply the division lemma to get
319 = 47 x 6 + 37
We consider the new divisor 47 and the new remainder 37,and apply the division lemma to get
47 = 37 x 1 + 10
We consider the new divisor 37 and the new remainder 10,and apply the division lemma to get
37 = 10 x 3 + 7
We consider the new divisor 10 and the new remainder 7,and apply the division lemma to get
10 = 7 x 1 + 3
We consider the new divisor 7 and the new remainder 3,and apply the division lemma to get
7 = 3 x 2 + 1
We consider the new divisor 3 and the new remainder 1,and apply the division lemma to get
3 = 1 x 3 + 0
The remainder has now become zero, so our procedure stops. Since the divisor at this stage is 1, the HCF of 8962 and 6813 is 1
Notice that 1 = HCF(3,1) = HCF(7,3) = HCF(10,7) = HCF(37,10) = HCF(47,37) = HCF(319,47) = HCF(366,319) = HCF(2149,366) = HCF(6813,2149) = HCF(8962,6813) .
We can take hcf of as 1st numbers and next number as another number to apply in Euclidean lemma
Step 1: Since 22710 > 1, we apply the division lemma to 22710 and 1, to get
22710 = 1 x 22710 + 0
The remainder has now become zero, so our procedure stops. Since the divisor at this stage is 1, the HCF of 1 and 22710 is 1
Notice that 1 = HCF(22710,1) .
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Frequently Asked Questions on HCF of 8962, 6813, 22710 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 8962, 6813, 22710?
Answer: HCF of 8962, 6813, 22710 is 1 the largest number that divides all the numbers leaving a remainder zero.
3. How to find HCF of 8962, 6813, 22710 using Euclid's Algorithm?
Answer: For arbitrary numbers 8962, 6813, 22710 apply Euclid’s Division Lemma in succession until you obtain a remainder zero. HCF is the remainder in the last but one step.