Highest Common Factor of 460, 6831 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 460, 6831 i.e. 23 the largest integer that leaves a remainder zero for all numbers.
HCF of 460, 6831 is 23 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 460, 6831 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 460, 6831 is 23.
HCF(460, 6831) = 23
HCF of 460, 6831 using Euclid's algorithm
Highest common factor or Highest common divisor (hcd) can be calculated by Euclid's algotithm.
Highest common factor (HCF) of 460, 6831 is 23.
Highest Common Factor of 460,6831 is 23
Step 1: Since 6831 > 460, we apply the division lemma to 6831 and 460, to get
6831 = 460 x 14 + 391
Step 2: Since the reminder 460 ≠ 0, we apply division lemma to 391 and 460, to get
460 = 391 x 1 + 69
Step 3: We consider the new divisor 391 and the new remainder 69, and apply the division lemma to get
391 = 69 x 5 + 46
We consider the new divisor 69 and the new remainder 46,and apply the division lemma to get
69 = 46 x 1 + 23
We consider the new divisor 46 and the new remainder 23,and apply the division lemma to get
46 = 23 x 2 + 0
The remainder has now become zero, so our procedure stops. Since the divisor at this stage is 23, the HCF of 460 and 6831 is 23
Notice that 23 = HCF(46,23) = HCF(69,46) = HCF(391,69) = HCF(460,391) = HCF(6831,460) .
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Frequently Asked Questions on HCF of 460, 6831 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 460, 6831?
Answer: HCF of 460, 6831 is 23 the largest number that divides all the numbers leaving a remainder zero.
3. How to find HCF of 460, 6831 using Euclid's Algorithm?
Answer: For arbitrary numbers 460, 6831 apply Euclid’s Division Lemma in succession until you obtain a remainder zero. HCF is the remainder in the last but one step.