Highest Common Factor of 746, 486, 668 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, 486, 668 i.e. 2 the largest integer that leaves a remainder zero for all numbers.

HCF of 746, 486, 668 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, 486, 668 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, 486, 668 is 2.

HCF(746, 486, 668) = 2

HCF of 746, 486, 668 using Euclid's algorithm

Highest common factor or Highest common divisor (hcd) can be calculated by Euclid's algotithm.

HCF of:

Highest common factor (HCF) of 746, 486, 668 is 2.

Highest Common Factor of 746,486,668 using Euclid's algorithm

Highest Common Factor of 746,486,668 is 2

Step 1: Since 746 > 486, we apply the division lemma to 746 and 486, to get

746 = 486 x 1 + 260

Step 2: Since the reminder 486 ≠ 0, we apply division lemma to 260 and 486, to get

486 = 260 x 1 + 226

Step 3: We consider the new divisor 260 and the new remainder 226, and apply the division lemma to get

260 = 226 x 1 + 34

We consider the new divisor 226 and the new remainder 34,and apply the division lemma to get

226 = 34 x 6 + 22

We consider the new divisor 34 and the new remainder 22,and apply the division lemma to get

34 = 22 x 1 + 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 746 and 486 is 2

Notice that 2 = HCF(10,2) = HCF(12,10) = HCF(22,12) = HCF(34,22) = HCF(226,34) = HCF(260,226) = HCF(486,260) = HCF(746,486) .

We can take hcf of as 1st numbers and next number as another number to apply in Euclidean lemma

Step 1: Since 668 > 2, we apply the division lemma to 668 and 2, to get

668 = 2 x 334 + 0

The remainder has now become zero, so our procedure stops. Since the divisor at this stage is 2, the HCF of 2 and 668 is 2

Notice that 2 = HCF(668,2) .

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Frequently Asked Questions on HCF of 746, 486, 668 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, 486, 668?

Answer: HCF of 746, 486, 668 is 2 the largest number that divides all the numbers leaving a remainder zero.

3. How to find HCF of 746, 486, 668 using Euclid's Algorithm?

Answer: For arbitrary numbers 746, 486, 668 apply Euclid’s Division Lemma in succession until you obtain a remainder zero. HCF is the remainder in the last but one step.