Highest Common Factor of 772, 304, 747 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, 304, 747 i.e. 1 the largest integer that leaves a remainder zero for all numbers.

HCF of 772, 304, 747 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, 304, 747 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, 304, 747 is 1.

HCF(772, 304, 747) = 1

HCF of 772, 304, 747 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, 304, 747 is 1.

Highest Common Factor of 772,304,747 using Euclid's algorithm

Highest Common Factor of 772,304,747 is 1

Step 1: Since 772 > 304, we apply the division lemma to 772 and 304, to get

772 = 304 x 2 + 164

Step 2: Since the reminder 304 ≠ 0, we apply division lemma to 164 and 304, to get

304 = 164 x 1 + 140

Step 3: We consider the new divisor 164 and the new remainder 140, and apply the division lemma to get

164 = 140 x 1 + 24

We consider the new divisor 140 and the new remainder 24,and apply the division lemma to get

140 = 24 x 5 + 20

We consider the new divisor 24 and the new remainder 20,and apply the division lemma to get

24 = 20 x 1 + 4

We consider the new divisor 20 and the new remainder 4,and apply the division lemma to get

20 = 4 x 5 + 0

The remainder has now become zero, so our procedure stops. Since the divisor at this stage is 4, the HCF of 772 and 304 is 4

Notice that 4 = HCF(20,4) = HCF(24,20) = HCF(140,24) = HCF(164,140) = HCF(304,164) = HCF(772,304) .

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

Step 1: Since 747 > 4, we apply the division lemma to 747 and 4, to get

747 = 4 x 186 + 3

Step 2: Since the reminder 4 ≠ 0, we apply division lemma to 3 and 4, to get

4 = 3 x 1 + 1

Step 3: 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 4 and 747 is 1

Notice that 1 = HCF(3,1) = HCF(4,3) = HCF(747,4) .

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Frequently Asked Questions on HCF of 772, 304, 747 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, 304, 747?

Answer: HCF of 772, 304, 747 is 1 the largest number that divides all the numbers leaving a remainder zero.

3. How to find HCF of 772, 304, 747 using Euclid's Algorithm?

Answer: For arbitrary numbers 772, 304, 747 apply Euclid’s Division Lemma in succession until you obtain a remainder zero. HCF is the remainder in the last but one step.