Highest Common Factor of 772, 228, 97 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 772, 228, 97 i.e. 1 the largest integer that leaves a remainder zero for all numbers.

HCF of 772, 228, 97 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 772, 228, 97 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 772, 228, 97 is 1.

HCF(772, 228, 97) = 1

HCF of 772, 228, 97 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 772, 228, 97 is 1.

Highest Common Factor of 772,228,97 using Euclid's algorithm

Highest Common Factor of 772,228,97 is 1

Step 1: Since 772 > 228, we apply the division lemma to 772 and 228, to get

772 = 228 x 3 + 88

Step 2: Since the reminder 228 ≠ 0, we apply division lemma to 88 and 228, to get

228 = 88 x 2 + 52

Step 3: We consider the new divisor 88 and the new remainder 52, and apply the division lemma to get

88 = 52 x 1 + 36

We consider the new divisor 52 and the new remainder 36,and apply the division lemma to get

52 = 36 x 1 + 16

We consider the new divisor 36 and the new remainder 16,and apply the division lemma to get

36 = 16 x 2 + 4

We consider the new divisor 16 and the new remainder 4,and apply the division lemma to get

16 = 4 x 4 + 0

The remainder has now become zero, so our procedure stops. Since the divisor at this stage is 4, the HCF of 772 and 228 is 4

Notice that 4 = HCF(16,4) = HCF(36,16) = HCF(52,36) = HCF(88,52) = HCF(228,88) = HCF(772,228) .

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

Step 1: Since 97 > 4, we apply the division lemma to 97 and 4, to get

97 = 4 x 24 + 1

Step 2: Since the reminder 4 ≠ 0, we apply division lemma to 1 and 4, to get

4 = 1 x 4 + 0

The remainder has now become zero, so our procedure stops. Since the divisor at this stage is 1, the HCF of 4 and 97 is 1

Notice that 1 = HCF(4,1) = HCF(97,4) .

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Frequently Asked Questions on HCF of 772, 228, 97 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 772, 228, 97?

Answer: HCF of 772, 228, 97 is 1 the largest number that divides all the numbers leaving a remainder zero.

3. How to find HCF of 772, 228, 97 using Euclid's Algorithm?

Answer: For arbitrary numbers 772, 228, 97 apply Euclid’s Division Lemma in succession until you obtain a remainder zero. HCF is the remainder in the last but one step.