Highest Common Factor of 684, 5374, 8967 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 684, 5374, 8967 i.e. 1 the largest integer that leaves a remainder zero for all numbers.
HCF of 684, 5374, 8967 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 684, 5374, 8967 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 684, 5374, 8967 is 1.
HCF(684, 5374, 8967) = 1
HCF of 684, 5374, 8967 using Euclid's algorithm
Highest common factor or Highest common divisor (hcd) can be calculated by Euclid's algotithm.
Highest common factor (HCF) of 684, 5374, 8967 is 1.
Highest Common Factor of 684,5374,8967 is 1
Step 1: Since 5374 > 684, we apply the division lemma to 5374 and 684, to get
5374 = 684 x 7 + 586
Step 2: Since the reminder 684 ≠ 0, we apply division lemma to 586 and 684, to get
684 = 586 x 1 + 98
Step 3: We consider the new divisor 586 and the new remainder 98, and apply the division lemma to get
586 = 98 x 5 + 96
We consider the new divisor 98 and the new remainder 96,and apply the division lemma to get
98 = 96 x 1 + 2
We consider the new divisor 96 and the new remainder 2,and apply the division lemma to get
96 = 2 x 48 + 0
The remainder has now become zero, so our procedure stops. Since the divisor at this stage is 2, the HCF of 684 and 5374 is 2
Notice that 2 = HCF(96,2) = HCF(98,96) = HCF(586,98) = HCF(684,586) = HCF(5374,684) .
We can take hcf of as 1st numbers and next number as another number to apply in Euclidean lemma
Step 1: Since 8967 > 2, we apply the division lemma to 8967 and 2, to get
8967 = 2 x 4483 + 1
Step 2: Since the reminder 2 ≠ 0, we apply division lemma to 1 and 2, 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 2 and 8967 is 1
Notice that 1 = HCF(2,1) = HCF(8967,2) .
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Frequently Asked Questions on HCF of 684, 5374, 8967 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 684, 5374, 8967?
Answer: HCF of 684, 5374, 8967 is 1 the largest number that divides all the numbers leaving a remainder zero.
3. How to find HCF of 684, 5374, 8967 using Euclid's Algorithm?
Answer: For arbitrary numbers 684, 5374, 8967 apply Euclid’s Division Lemma in succession until you obtain a remainder zero. HCF is the remainder in the last but one step.
