Highest Common Factor of 656, 8431, 8154 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 656, 8431, 8154 i.e. 1 the largest integer that leaves a remainder zero for all numbers.
HCF of 656, 8431, 8154 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 656, 8431, 8154 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 656, 8431, 8154 is 1.
HCF(656, 8431, 8154) = 1
HCF of 656, 8431, 8154 using Euclid's algorithm
Highest common factor or Highest common divisor (hcd) can be calculated by Euclid's algotithm.
Highest common factor (HCF) of 656, 8431, 8154 is 1.
Highest Common Factor of 656,8431,8154 is 1
Step 1: Since 8431 > 656, we apply the division lemma to 8431 and 656, to get
8431 = 656 x 12 + 559
Step 2: Since the reminder 656 ≠ 0, we apply division lemma to 559 and 656, to get
656 = 559 x 1 + 97
Step 3: We consider the new divisor 559 and the new remainder 97, and apply the division lemma to get
559 = 97 x 5 + 74
We consider the new divisor 97 and the new remainder 74,and apply the division lemma to get
97 = 74 x 1 + 23
We consider the new divisor 74 and the new remainder 23,and apply the division lemma to get
74 = 23 x 3 + 5
We consider the new divisor 23 and the new remainder 5,and apply the division lemma to get
23 = 5 x 4 + 3
We consider the new divisor 5 and the new remainder 3,and apply the division lemma to get
5 = 3 x 1 + 2
We consider the new divisor 3 and the new remainder 2,and apply the division lemma to get
3 = 2 x 1 + 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 656 and 8431 is 1
Notice that 1 = HCF(2,1) = HCF(3,2) = HCF(5,3) = HCF(23,5) = HCF(74,23) = HCF(97,74) = HCF(559,97) = HCF(656,559) = HCF(8431,656) .
We can take hcf of as 1st numbers and next number as another number to apply in Euclidean lemma
Step 1: Since 8154 > 1, we apply the division lemma to 8154 and 1, to get
8154 = 1 x 8154 + 0
The remainder has now become zero, so our procedure stops. Since the divisor at this stage is 1, the HCF of 1 and 8154 is 1
Notice that 1 = HCF(8154,1) .
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Frequently Asked Questions on HCF of 656, 8431, 8154 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 656, 8431, 8154?
Answer: HCF of 656, 8431, 8154 is 1 the largest number that divides all the numbers leaving a remainder zero.
3. How to find HCF of 656, 8431, 8154 using Euclid's Algorithm?
Answer: For arbitrary numbers 656, 8431, 8154 apply Euclid’s Division Lemma in succession until you obtain a remainder zero. HCF is the remainder in the last but one step.
