Highest Common Factor of 831, 2154 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 831, 2154 i.e. 3 the largest integer that leaves a remainder zero for all numbers.
HCF of 831, 2154 is 3 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 831, 2154 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 831, 2154 is 3.
HCF(831, 2154) = 3
HCF of 831, 2154 using Euclid's algorithm
Highest common factor or Highest common divisor (hcd) can be calculated by Euclid's algotithm.
Highest common factor (HCF) of 831, 2154 is 3.
Highest Common Factor of 831,2154 is 3
Step 1: Since 2154 > 831, we apply the division lemma to 2154 and 831, to get
2154 = 831 x 2 + 492
Step 2: Since the reminder 831 ≠ 0, we apply division lemma to 492 and 831, to get
831 = 492 x 1 + 339
Step 3: We consider the new divisor 492 and the new remainder 339, and apply the division lemma to get
492 = 339 x 1 + 153
We consider the new divisor 339 and the new remainder 153,and apply the division lemma to get
339 = 153 x 2 + 33
We consider the new divisor 153 and the new remainder 33,and apply the division lemma to get
153 = 33 x 4 + 21
We consider the new divisor 33 and the new remainder 21,and apply the division lemma to get
33 = 21 x 1 + 12
We consider the new divisor 21 and the new remainder 12,and apply the division lemma to get
21 = 12 x 1 + 9
We consider the new divisor 12 and the new remainder 9,and apply the division lemma to get
12 = 9 x 1 + 3
We consider the new divisor 9 and the new remainder 3,and apply the division lemma to get
9 = 3 x 3 + 0
The remainder has now become zero, so our procedure stops. Since the divisor at this stage is 3, the HCF of 831 and 2154 is 3
Notice that 3 = HCF(9,3) = HCF(12,9) = HCF(21,12) = HCF(33,21) = HCF(153,33) = HCF(339,153) = HCF(492,339) = HCF(831,492) = HCF(2154,831) .
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Frequently Asked Questions on HCF of 831, 2154 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 831, 2154?
Answer: HCF of 831, 2154 is 3 the largest number that divides all the numbers leaving a remainder zero.
3. How to find HCF of 831, 2154 using Euclid's Algorithm?
Answer: For arbitrary numbers 831, 2154 apply Euclid’s Division Lemma in succession until you obtain a remainder zero. HCF is the remainder in the last but one step.