Highest Common Factor of 684, 428, 364 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, 428, 364 i.e. 4 the largest integer that leaves a remainder zero for all numbers.
HCF of 684, 428, 364 is 4 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, 428, 364 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, 428, 364 is 4.
HCF(684, 428, 364) = 4
HCF of 684, 428, 364 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, 428, 364 is 4.
Highest Common Factor of 684,428,364 is 4
Step 1: Since 684 > 428, we apply the division lemma to 684 and 428, to get
684 = 428 x 1 + 256
Step 2: Since the reminder 428 ≠ 0, we apply division lemma to 256 and 428, to get
428 = 256 x 1 + 172
Step 3: We consider the new divisor 256 and the new remainder 172, and apply the division lemma to get
256 = 172 x 1 + 84
We consider the new divisor 172 and the new remainder 84,and apply the division lemma to get
172 = 84 x 2 + 4
We consider the new divisor 84 and the new remainder 4,and apply the division lemma to get
84 = 4 x 21 + 0
The remainder has now become zero, so our procedure stops. Since the divisor at this stage is 4, the HCF of 684 and 428 is 4
Notice that 4 = HCF(84,4) = HCF(172,84) = HCF(256,172) = HCF(428,256) = HCF(684,428) .
We can take hcf of as 1st numbers and next number as another number to apply in Euclidean lemma
Step 1: Since 364 > 4, we apply the division lemma to 364 and 4, to get
364 = 4 x 91 + 0
The remainder has now become zero, so our procedure stops. Since the divisor at this stage is 4, the HCF of 4 and 364 is 4
Notice that 4 = HCF(364,4) .
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Frequently Asked Questions on HCF of 684, 428, 364 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, 428, 364?
Answer: HCF of 684, 428, 364 is 4 the largest number that divides all the numbers leaving a remainder zero.
3. How to find HCF of 684, 428, 364 using Euclid's Algorithm?
Answer: For arbitrary numbers 684, 428, 364 apply Euclid’s Division Lemma in succession until you obtain a remainder zero. HCF is the remainder in the last but one step.