Highest Common Factor of 746, 283, 308 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, 283, 308 i.e. 1 the largest integer that leaves a remainder zero for all numbers.

HCF of 746, 283, 308 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 746, 283, 308 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, 283, 308 is 1.

HCF(746, 283, 308) = 1

HCF of 746, 283, 308 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, 283, 308 is 1.

Highest Common Factor of 746,283,308 using Euclid's algorithm

Highest Common Factor of 746,283,308 is 1

Step 1: Since 746 > 283, we apply the division lemma to 746 and 283, to get

746 = 283 x 2 + 180

Step 2: Since the reminder 283 ≠ 0, we apply division lemma to 180 and 283, to get

283 = 180 x 1 + 103

Step 3: We consider the new divisor 180 and the new remainder 103, and apply the division lemma to get

180 = 103 x 1 + 77

We consider the new divisor 103 and the new remainder 77,and apply the division lemma to get

103 = 77 x 1 + 26

We consider the new divisor 77 and the new remainder 26,and apply the division lemma to get

77 = 26 x 2 + 25

We consider the new divisor 26 and the new remainder 25,and apply the division lemma to get

26 = 25 x 1 + 1

We consider the new divisor 25 and the new remainder 1,and apply the division lemma to get

25 = 1 x 25 + 0

The remainder has now become zero, so our procedure stops. Since the divisor at this stage is 1, the HCF of 746 and 283 is 1

Notice that 1 = HCF(25,1) = HCF(26,25) = HCF(77,26) = HCF(103,77) = HCF(180,103) = HCF(283,180) = HCF(746,283) .

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

Step 1: Since 308 > 1, we apply the division lemma to 308 and 1, to get

308 = 1 x 308 + 0

The remainder has now become zero, so our procedure stops. Since the divisor at this stage is 1, the HCF of 1 and 308 is 1

Notice that 1 = HCF(308,1) .

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Frequently Asked Questions on HCF of 746, 283, 308 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, 283, 308?

Answer: HCF of 746, 283, 308 is 1 the largest number that divides all the numbers leaving a remainder zero.

3. How to find HCF of 746, 283, 308 using Euclid's Algorithm?

Answer: For arbitrary numbers 746, 283, 308 apply Euclid’s Division Lemma in succession until you obtain a remainder zero. HCF is the remainder in the last but one step.