Highest Common Factor of 277, 748, 85 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 277, 748, 85 i.e. 1 the largest integer that leaves a remainder zero for all numbers.

HCF of 277, 748, 85 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 277, 748, 85 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 277, 748, 85 is 1.

HCF(277, 748, 85) = 1

HCF of 277, 748, 85 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 277, 748, 85 is 1.

Highest Common Factor of 277,748,85 using Euclid's algorithm

Highest Common Factor of 277,748,85 is 1

Step 1: Since 748 > 277, we apply the division lemma to 748 and 277, to get

748 = 277 x 2 + 194

Step 2: Since the reminder 277 ≠ 0, we apply division lemma to 194 and 277, to get

277 = 194 x 1 + 83

Step 3: We consider the new divisor 194 and the new remainder 83, and apply the division lemma to get

194 = 83 x 2 + 28

We consider the new divisor 83 and the new remainder 28,and apply the division lemma to get

83 = 28 x 2 + 27

We consider the new divisor 28 and the new remainder 27,and apply the division lemma to get

28 = 27 x 1 + 1

We consider the new divisor 27 and the new remainder 1,and apply the division lemma to get

27 = 1 x 27 + 0

The remainder has now become zero, so our procedure stops. Since the divisor at this stage is 1, the HCF of 277 and 748 is 1

Notice that 1 = HCF(27,1) = HCF(28,27) = HCF(83,28) = HCF(194,83) = HCF(277,194) = HCF(748,277) .

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

Step 1: Since 85 > 1, we apply the division lemma to 85 and 1, to get

85 = 1 x 85 + 0

The remainder has now become zero, so our procedure stops. Since the divisor at this stage is 1, the HCF of 1 and 85 is 1

Notice that 1 = HCF(85,1) .

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Frequently Asked Questions on HCF of 277, 748, 85 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 277, 748, 85?

Answer: HCF of 277, 748, 85 is 1 the largest number that divides all the numbers leaving a remainder zero.

3. How to find HCF of 277, 748, 85 using Euclid's Algorithm?

Answer: For arbitrary numbers 277, 748, 85 apply Euclid’s Division Lemma in succession until you obtain a remainder zero. HCF is the remainder in the last but one step.