Highest Common Factor of 846, 21632 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 846, 21632 i.e. 2 the largest integer that leaves a remainder zero for all numbers.
HCF of 846, 21632 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 846, 21632 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 846, 21632 is 2.
HCF(846, 21632) = 2
HCF of 846, 21632 using Euclid's algorithm
Highest common factor or Highest common divisor (hcd) can be calculated by Euclid's algotithm.
Highest common factor (HCF) of 846, 21632 is 2.
Highest Common Factor of 846,21632 is 2
Step 1: Since 21632 > 846, we apply the division lemma to 21632 and 846, to get
21632 = 846 x 25 + 482
Step 2: Since the reminder 846 ≠ 0, we apply division lemma to 482 and 846, to get
846 = 482 x 1 + 364
Step 3: We consider the new divisor 482 and the new remainder 364, and apply the division lemma to get
482 = 364 x 1 + 118
We consider the new divisor 364 and the new remainder 118,and apply the division lemma to get
364 = 118 x 3 + 10
We consider the new divisor 118 and the new remainder 10,and apply the division lemma to get
118 = 10 x 11 + 8
We consider the new divisor 10 and the new remainder 8,and apply the division lemma to get
10 = 8 x 1 + 2
We consider the new divisor 8 and the new remainder 2,and apply the division lemma to get
8 = 2 x 4 + 0
The remainder has now become zero, so our procedure stops. Since the divisor at this stage is 2, the HCF of 846 and 21632 is 2
Notice that 2 = HCF(8,2) = HCF(10,8) = HCF(118,10) = HCF(364,118) = HCF(482,364) = HCF(846,482) = HCF(21632,846) .
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Frequently Asked Questions on HCF of 846, 21632 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 846, 21632?
Answer: HCF of 846, 21632 is 2 the largest number that divides all the numbers leaving a remainder zero.
3. How to find HCF of 846, 21632 using Euclid's Algorithm?
Answer: For arbitrary numbers 846, 21632 apply Euclid’s Division Lemma in succession until you obtain a remainder zero. HCF is the remainder in the last but one step.