Highest Common Factor of 3131, 9728 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 3131, 9728 i.e. 1 the largest integer that leaves a remainder zero for all numbers.
HCF of 3131, 9728 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 3131, 9728 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 3131, 9728 is 1.
HCF(3131, 9728) = 1
HCF of 3131, 9728 using Euclid's algorithm
Highest common factor or Highest common divisor (hcd) can be calculated by Euclid's algotithm.
Highest common factor (HCF) of 3131, 9728 is 1.
Highest Common Factor of 3131,9728 is 1
Step 1: Since 9728 > 3131, we apply the division lemma to 9728 and 3131, to get
9728 = 3131 x 3 + 335
Step 2: Since the reminder 3131 ≠ 0, we apply division lemma to 335 and 3131, to get
3131 = 335 x 9 + 116
Step 3: We consider the new divisor 335 and the new remainder 116, and apply the division lemma to get
335 = 116 x 2 + 103
We consider the new divisor 116 and the new remainder 103,and apply the division lemma to get
116 = 103 x 1 + 13
We consider the new divisor 103 and the new remainder 13,and apply the division lemma to get
103 = 13 x 7 + 12
We consider the new divisor 13 and the new remainder 12,and apply the division lemma to get
13 = 12 x 1 + 1
We consider the new divisor 12 and the new remainder 1,and apply the division lemma to get
12 = 1 x 12 + 0
The remainder has now become zero, so our procedure stops. Since the divisor at this stage is 1, the HCF of 3131 and 9728 is 1
Notice that 1 = HCF(12,1) = HCF(13,12) = HCF(103,13) = HCF(116,103) = HCF(335,116) = HCF(3131,335) = HCF(9728,3131) .
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Frequently Asked Questions on HCF of 3131, 9728 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 3131, 9728?
Answer: HCF of 3131, 9728 is 1 the largest number that divides all the numbers leaving a remainder zero.
3. How to find HCF of 3131, 9728 using Euclid's Algorithm?
Answer: For arbitrary numbers 3131, 9728 apply Euclid’s Division Lemma in succession until you obtain a remainder zero. HCF is the remainder in the last but one step.
