Highest Common Factor of 3646, 4277, 31177 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 3646, 4277, 31177 i.e. 1 the largest integer that leaves a remainder zero for all numbers.
HCF of 3646, 4277, 31177 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 3646, 4277, 31177 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 3646, 4277, 31177 is 1.
HCF(3646, 4277, 31177) = 1
HCF of 3646, 4277, 31177 using Euclid's algorithm
Highest common factor or Highest common divisor (hcd) can be calculated by Euclid's algotithm.
Highest common factor (HCF) of 3646, 4277, 31177 is 1.
Highest Common Factor of 3646,4277,31177 is 1
Step 1: Since 4277 > 3646, we apply the division lemma to 4277 and 3646, to get
4277 = 3646 x 1 + 631
Step 2: Since the reminder 3646 ≠ 0, we apply division lemma to 631 and 3646, to get
3646 = 631 x 5 + 491
Step 3: We consider the new divisor 631 and the new remainder 491, and apply the division lemma to get
631 = 491 x 1 + 140
We consider the new divisor 491 and the new remainder 140,and apply the division lemma to get
491 = 140 x 3 + 71
We consider the new divisor 140 and the new remainder 71,and apply the division lemma to get
140 = 71 x 1 + 69
We consider the new divisor 71 and the new remainder 69,and apply the division lemma to get
71 = 69 x 1 + 2
We consider the new divisor 69 and the new remainder 2,and apply the division lemma to get
69 = 2 x 34 + 1
We consider the new divisor 2 and the new remainder 1,and apply the division lemma to get
2 = 1 x 2 + 0
The remainder has now become zero, so our procedure stops. Since the divisor at this stage is 1, the HCF of 3646 and 4277 is 1
Notice that 1 = HCF(2,1) = HCF(69,2) = HCF(71,69) = HCF(140,71) = HCF(491,140) = HCF(631,491) = HCF(3646,631) = HCF(4277,3646) .
We can take hcf of as 1st numbers and next number as another number to apply in Euclidean lemma
Step 1: Since 31177 > 1, we apply the division lemma to 31177 and 1, to get
31177 = 1 x 31177 + 0
The remainder has now become zero, so our procedure stops. Since the divisor at this stage is 1, the HCF of 1 and 31177 is 1
Notice that 1 = HCF(31177,1) .
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Frequently Asked Questions on HCF of 3646, 4277, 31177 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 3646, 4277, 31177?
Answer: HCF of 3646, 4277, 31177 is 1 the largest number that divides all the numbers leaving a remainder zero.
3. How to find HCF of 3646, 4277, 31177 using Euclid's Algorithm?
Answer: For arbitrary numbers 3646, 4277, 31177 apply Euclid’s Division Lemma in succession until you obtain a remainder zero. HCF is the remainder in the last but one step.