Highest Common Factor of 656, 378 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, 378 i.e. 2 the largest integer that leaves a remainder zero for all numbers.
HCF of 656, 378 is 2 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, 378 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, 378 is 2.
HCF(656, 378) = 2
HCF of 656, 378 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, 378 is 2.
Highest Common Factor of 656,378 is 2
Step 1: Since 656 > 378, we apply the division lemma to 656 and 378, to get
656 = 378 x 1 + 278
Step 2: Since the reminder 378 ≠ 0, we apply division lemma to 278 and 378, to get
378 = 278 x 1 + 100
Step 3: We consider the new divisor 278 and the new remainder 100, and apply the division lemma to get
278 = 100 x 2 + 78
We consider the new divisor 100 and the new remainder 78,and apply the division lemma to get
100 = 78 x 1 + 22
We consider the new divisor 78 and the new remainder 22,and apply the division lemma to get
78 = 22 x 3 + 12
We consider the new divisor 22 and the new remainder 12,and apply the division lemma to get
22 = 12 x 1 + 10
We consider the new divisor 12 and the new remainder 10,and apply the division lemma to get
12 = 10 x 1 + 2
We consider the new divisor 10 and the new remainder 2,and apply the division lemma to get
10 = 2 x 5 + 0
The remainder has now become zero, so our procedure stops. Since the divisor at this stage is 2, the HCF of 656 and 378 is 2
Notice that 2 = HCF(10,2) = HCF(12,10) = HCF(22,12) = HCF(78,22) = HCF(100,78) = HCF(278,100) = HCF(378,278) = HCF(656,378) .
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Frequently Asked Questions on HCF of 656, 378 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, 378?
Answer: HCF of 656, 378 is 2 the largest number that divides all the numbers leaving a remainder zero.
3. How to find HCF of 656, 378 using Euclid's Algorithm?
Answer: For arbitrary numbers 656, 378 apply Euclid’s Division Lemma in succession until you obtain a remainder zero. HCF is the remainder in the last but one step.
