Highest Common Factor of 747, 974, 493, 78 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 747, 974, 493, 78 i.e. 1 the largest integer that leaves a remainder zero for all numbers.

HCF of 747, 974, 493, 78 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 747, 974, 493, 78 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 747, 974, 493, 78 is 1.

HCF(747, 974, 493, 78) = 1

HCF of 747, 974, 493, 78 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 747, 974, 493, 78 is 1.

Highest Common Factor of 747,974,493,78 using Euclid's algorithm

Highest Common Factor of 747,974,493,78 is 1

Step 1: Since 974 > 747, we apply the division lemma to 974 and 747, to get

974 = 747 x 1 + 227

Step 2: Since the reminder 747 ≠ 0, we apply division lemma to 227 and 747, to get

747 = 227 x 3 + 66

Step 3: We consider the new divisor 227 and the new remainder 66, and apply the division lemma to get

227 = 66 x 3 + 29

We consider the new divisor 66 and the new remainder 29,and apply the division lemma to get

66 = 29 x 2 + 8

We consider the new divisor 29 and the new remainder 8,and apply the division lemma to get

29 = 8 x 3 + 5

We consider the new divisor 8 and the new remainder 5,and apply the division lemma to get

8 = 5 x 1 + 3

We consider the new divisor 5 and the new remainder 3,and apply the division lemma to get

5 = 3 x 1 + 2

We consider the new divisor 3 and the new remainder 2,and apply the division lemma to get

3 = 2 x 1 + 1

We consider the new divisor 2 and the new remainder 1,and apply the division lemma to get

2 = 1 x 2 + 0

The remainder has now become zero, so our procedure stops. Since the divisor at this stage is 1, the HCF of 747 and 974 is 1

Notice that 1 = HCF(2,1) = HCF(3,2) = HCF(5,3) = HCF(8,5) = HCF(29,8) = HCF(66,29) = HCF(227,66) = HCF(747,227) = HCF(974,747) .

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

Step 1: Since 493 > 1, we apply the division lemma to 493 and 1, to get

493 = 1 x 493 + 0

The remainder has now become zero, so our procedure stops. Since the divisor at this stage is 1, the HCF of 1 and 493 is 1

Notice that 1 = HCF(493,1) .

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

Step 1: Since 78 > 1, we apply the division lemma to 78 and 1, to get

78 = 1 x 78 + 0

The remainder has now become zero, so our procedure stops. Since the divisor at this stage is 1, the HCF of 1 and 78 is 1

Notice that 1 = HCF(78,1) .

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Frequently Asked Questions on HCF of 747, 974, 493, 78 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 747, 974, 493, 78?

Answer: HCF of 747, 974, 493, 78 is 1 the largest number that divides all the numbers leaving a remainder zero.

3. How to find HCF of 747, 974, 493, 78 using Euclid's Algorithm?

Answer: For arbitrary numbers 747, 974, 493, 78 apply Euclid’s Division Lemma in succession until you obtain a remainder zero. HCF is the remainder in the last but one step.