Highest Common Factor of 757, 308, 267 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 757, 308, 267 i.e. 1 the largest integer that leaves a remainder zero for all numbers.

HCF of 757, 308, 267 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 757, 308, 267 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 757, 308, 267 is 1.

HCF(757, 308, 267) = 1

HCF of 757, 308, 267 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 757, 308, 267 is 1.

Highest Common Factor of 757,308,267 using Euclid's algorithm

Highest Common Factor of 757,308,267 is 1

Step 1: Since 757 > 308, we apply the division lemma to 757 and 308, to get

757 = 308 x 2 + 141

Step 2: Since the reminder 308 ≠ 0, we apply division lemma to 141 and 308, to get

308 = 141 x 2 + 26

Step 3: We consider the new divisor 141 and the new remainder 26, and apply the division lemma to get

141 = 26 x 5 + 11

We consider the new divisor 26 and the new remainder 11,and apply the division lemma to get

26 = 11 x 2 + 4

We consider the new divisor 11 and the new remainder 4,and apply the division lemma to get

11 = 4 x 2 + 3

We consider the new divisor 4 and the new remainder 3,and apply the division lemma to get

4 = 3 x 1 + 1

We consider the new divisor 3 and the new remainder 1,and apply the division lemma to get

3 = 1 x 3 + 0

The remainder has now become zero, so our procedure stops. Since the divisor at this stage is 1, the HCF of 757 and 308 is 1

Notice that 1 = HCF(3,1) = HCF(4,3) = HCF(11,4) = HCF(26,11) = HCF(141,26) = HCF(308,141) = HCF(757,308) .

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

Step 1: Since 267 > 1, we apply the division lemma to 267 and 1, to get

267 = 1 x 267 + 0

The remainder has now become zero, so our procedure stops. Since the divisor at this stage is 1, the HCF of 1 and 267 is 1

Notice that 1 = HCF(267,1) .

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Frequently Asked Questions on HCF of 757, 308, 267 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 757, 308, 267?

Answer: HCF of 757, 308, 267 is 1 the largest number that divides all the numbers leaving a remainder zero.

3. How to find HCF of 757, 308, 267 using Euclid's Algorithm?

Answer: For arbitrary numbers 757, 308, 267 apply Euclid’s Division Lemma in succession until you obtain a remainder zero. HCF is the remainder in the last but one step.