Highest Common Factor of 6461, 974 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 6461, 974 i.e. 1 the largest integer that leaves a remainder zero for all numbers.
HCF of 6461, 974 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 6461, 974 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 6461, 974 is 1.
HCF(6461, 974) = 1
HCF of 6461, 974 using Euclid's algorithm
Highest common factor or Highest common divisor (hcd) can be calculated by Euclid's algotithm.
Highest common factor (HCF) of 6461, 974 is 1.
Highest Common Factor of 6461,974 is 1
Step 1: Since 6461 > 974, we apply the division lemma to 6461 and 974, to get
6461 = 974 x 6 + 617
Step 2: Since the reminder 974 ≠ 0, we apply division lemma to 617 and 974, to get
974 = 617 x 1 + 357
Step 3: We consider the new divisor 617 and the new remainder 357, and apply the division lemma to get
617 = 357 x 1 + 260
We consider the new divisor 357 and the new remainder 260,and apply the division lemma to get
357 = 260 x 1 + 97
We consider the new divisor 260 and the new remainder 97,and apply the division lemma to get
260 = 97 x 2 + 66
We consider the new divisor 97 and the new remainder 66,and apply the division lemma to get
97 = 66 x 1 + 31
We consider the new divisor 66 and the new remainder 31,and apply the division lemma to get
66 = 31 x 2 + 4
We consider the new divisor 31 and the new remainder 4,and apply the division lemma to get
31 = 4 x 7 + 3
We consider the new divisor 4 and the new remainder 3,and apply the division lemma to get
4 = 3 x 1 + 1
We consider the new divisor 3 and the new remainder 1,and apply the division lemma to get
3 = 1 x 3 + 0
The remainder has now become zero, so our procedure stops. Since the divisor at this stage is 1, the HCF of 6461 and 974 is 1
Notice that 1 = HCF(3,1) = HCF(4,3) = HCF(31,4) = HCF(66,31) = HCF(97,66) = HCF(260,97) = HCF(357,260) = HCF(617,357) = HCF(974,617) = HCF(6461,974) .
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Frequently Asked Questions on HCF of 6461, 974 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 6461, 974?
Answer: HCF of 6461, 974 is 1 the largest number that divides all the numbers leaving a remainder zero.
3. How to find HCF of 6461, 974 using Euclid's Algorithm?
Answer: For arbitrary numbers 6461, 974 apply Euclid’s Division Lemma in succession until you obtain a remainder zero. HCF is the remainder in the last but one step.