Highest Common Factor of 711, 754, 748 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 711, 754, 748 i.e. 1 the largest integer that leaves a remainder zero for all numbers.

HCF of 711, 754, 748 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 711, 754, 748 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 711, 754, 748 is 1.

HCF(711, 754, 748) = 1

HCF of 711, 754, 748 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 711, 754, 748 is 1.

Highest Common Factor of 711,754,748 using Euclid's algorithm

Highest Common Factor of 711,754,748 is 1

Step 1: Since 754 > 711, we apply the division lemma to 754 and 711, to get

754 = 711 x 1 + 43

Step 2: Since the reminder 711 ≠ 0, we apply division lemma to 43 and 711, to get

711 = 43 x 16 + 23

Step 3: We consider the new divisor 43 and the new remainder 23, and apply the division lemma to get

43 = 23 x 1 + 20

We consider the new divisor 23 and the new remainder 20,and apply the division lemma to get

23 = 20 x 1 + 3

We consider the new divisor 20 and the new remainder 3,and apply the division lemma to get

20 = 3 x 6 + 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 711 and 754 is 1

Notice that 1 = HCF(2,1) = HCF(3,2) = HCF(20,3) = HCF(23,20) = HCF(43,23) = HCF(711,43) = HCF(754,711) .

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

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

748 = 1 x 748 + 0

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

Notice that 1 = HCF(748,1) .

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Frequently Asked Questions on HCF of 711, 754, 748 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 711, 754, 748?

Answer: HCF of 711, 754, 748 is 1 the largest number that divides all the numbers leaving a remainder zero.

3. How to find HCF of 711, 754, 748 using Euclid's Algorithm?

Answer: For arbitrary numbers 711, 754, 748 apply Euclid’s Division Lemma in succession until you obtain a remainder zero. HCF is the remainder in the last but one step.