Highest Common Factor of 746, 268 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 746, 268 i.e. 2 the largest integer that leaves a remainder zero for all numbers.
HCF of 746, 268 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 746, 268 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 746, 268 is 2.
HCF(746, 268) = 2
HCF of 746, 268 using Euclid's algorithm
Highest common factor or Highest common divisor (hcd) can be calculated by Euclid's algotithm.
Highest common factor (HCF) of 746, 268 is 2.
Highest Common Factor of 746,268 is 2
Step 1: Since 746 > 268, we apply the division lemma to 746 and 268, to get
746 = 268 x 2 + 210
Step 2: Since the reminder 268 ≠ 0, we apply division lemma to 210 and 268, to get
268 = 210 x 1 + 58
Step 3: We consider the new divisor 210 and the new remainder 58, and apply the division lemma to get
210 = 58 x 3 + 36
We consider the new divisor 58 and the new remainder 36,and apply the division lemma to get
58 = 36 x 1 + 22
We consider the new divisor 36 and the new remainder 22,and apply the division lemma to get
36 = 22 x 1 + 14
We consider the new divisor 22 and the new remainder 14,and apply the division lemma to get
22 = 14 x 1 + 8
We consider the new divisor 14 and the new remainder 8,and apply the division lemma to get
14 = 8 x 1 + 6
We consider the new divisor 8 and the new remainder 6,and apply the division lemma to get
8 = 6 x 1 + 2
We consider the new divisor 6 and the new remainder 2,and apply the division lemma to get
6 = 2 x 3 + 0
The remainder has now become zero, so our procedure stops. Since the divisor at this stage is 2, the HCF of 746 and 268 is 2
Notice that 2 = HCF(6,2) = HCF(8,6) = HCF(14,8) = HCF(22,14) = HCF(36,22) = HCF(58,36) = HCF(210,58) = HCF(268,210) = HCF(746,268) .
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Frequently Asked Questions on HCF of 746, 268 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 746, 268?
Answer: HCF of 746, 268 is 2 the largest number that divides all the numbers leaving a remainder zero.
3. How to find HCF of 746, 268 using Euclid's Algorithm?
Answer: For arbitrary numbers 746, 268 apply Euclid’s Division Lemma in succession until you obtain a remainder zero. HCF is the remainder in the last but one step.