Highest Common Factor of 656, 205, 68 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, 205, 68 i.e. 1 the largest integer that leaves a remainder zero for all numbers.
HCF of 656, 205, 68 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, 205, 68 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, 205, 68 is 1.
HCF(656, 205, 68) = 1
HCF of 656, 205, 68 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, 205, 68 is 1.
Highest Common Factor of 656,205,68 is 1
Step 1: Since 656 > 205, we apply the division lemma to 656 and 205, to get
656 = 205 x 3 + 41
Step 2: Since the reminder 205 ≠ 0, we apply division lemma to 41 and 205, to get
205 = 41 x 5 + 0
The remainder has now become zero, so our procedure stops. Since the divisor at this stage is 41, the HCF of 656 and 205 is 41
Notice that 41 = HCF(205,41) = HCF(656,205) .
We can take hcf of as 1st numbers and next number as another number to apply in Euclidean lemma
Step 1: Since 68 > 41, we apply the division lemma to 68 and 41, to get
68 = 41 x 1 + 27
Step 2: Since the reminder 41 ≠ 0, we apply division lemma to 27 and 41, to get
41 = 27 x 1 + 14
Step 3: We consider the new divisor 27 and the new remainder 14, and apply the division lemma to get
27 = 14 x 1 + 13
We consider the new divisor 14 and the new remainder 13,and apply the division lemma to get
14 = 13 x 1 + 1
We consider the new divisor 13 and the new remainder 1,and apply the division lemma to get
13 = 1 x 13 + 0
The remainder has now become zero, so our procedure stops. Since the divisor at this stage is 1, the HCF of 41 and 68 is 1
Notice that 1 = HCF(13,1) = HCF(14,13) = HCF(27,14) = HCF(41,27) = HCF(68,41) .
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Frequently Asked Questions on HCF of 656, 205, 68 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, 205, 68?
Answer: HCF of 656, 205, 68 is 1 the largest number that divides all the numbers leaving a remainder zero.
3. How to find HCF of 656, 205, 68 using Euclid's Algorithm?
Answer: For arbitrary numbers 656, 205, 68 apply Euclid’s Division Lemma in succession until you obtain a remainder zero. HCF is the remainder in the last but one step.