Highest Common Factor of 6894, 9326, 21636 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 6894, 9326, 21636 i.e. 2 the largest integer that leaves a remainder zero for all numbers.
HCF of 6894, 9326, 21636 is 2 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 6894, 9326, 21636 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 6894, 9326, 21636 is 2.
HCF(6894, 9326, 21636) = 2
HCF of 6894, 9326, 21636 using Euclid's algorithm
Highest common factor or Highest common divisor (hcd) can be calculated by Euclid's algotithm.
Highest common factor (HCF) of 6894, 9326, 21636 is 2.
Highest Common Factor of 6894,9326,21636 is 2
Step 1: Since 9326 > 6894, we apply the division lemma to 9326 and 6894, to get
9326 = 6894 x 1 + 2432
Step 2: Since the reminder 6894 ≠ 0, we apply division lemma to 2432 and 6894, to get
6894 = 2432 x 2 + 2030
Step 3: We consider the new divisor 2432 and the new remainder 2030, and apply the division lemma to get
2432 = 2030 x 1 + 402
We consider the new divisor 2030 and the new remainder 402,and apply the division lemma to get
2030 = 402 x 5 + 20
We consider the new divisor 402 and the new remainder 20,and apply the division lemma to get
402 = 20 x 20 + 2
We consider the new divisor 20 and the new remainder 2,and apply the division lemma to get
20 = 2 x 10 + 0
The remainder has now become zero, so our procedure stops. Since the divisor at this stage is 2, the HCF of 6894 and 9326 is 2
Notice that 2 = HCF(20,2) = HCF(402,20) = HCF(2030,402) = HCF(2432,2030) = HCF(6894,2432) = HCF(9326,6894) .
We can take hcf of as 1st numbers and next number as another number to apply in Euclidean lemma
Step 1: Since 21636 > 2, we apply the division lemma to 21636 and 2, to get
21636 = 2 x 10818 + 0
The remainder has now become zero, so our procedure stops. Since the divisor at this stage is 2, the HCF of 2 and 21636 is 2
Notice that 2 = HCF(21636,2) .
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Frequently Asked Questions on HCF of 6894, 9326, 21636 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 6894, 9326, 21636?
Answer: HCF of 6894, 9326, 21636 is 2 the largest number that divides all the numbers leaving a remainder zero.
3. How to find HCF of 6894, 9326, 21636 using Euclid's Algorithm?
Answer: For arbitrary numbers 6894, 9326, 21636 apply Euclid’s Division Lemma in succession until you obtain a remainder zero. HCF is the remainder in the last but one step.