Highest Common Factor of 754, 332, 724 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 754, 332, 724 i.e. 2 the largest integer that leaves a remainder zero for all numbers.

HCF of 754, 332, 724 is 2 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 754, 332, 724 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 754, 332, 724 is 2.

HCF(754, 332, 724) = 2

HCF of 754, 332, 724 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 754, 332, 724 is 2.

Highest Common Factor of 754,332,724 using Euclid's algorithm

Highest Common Factor of 754,332,724 is 2

Step 1: Since 754 > 332, we apply the division lemma to 754 and 332, to get

754 = 332 x 2 + 90

Step 2: Since the reminder 332 ≠ 0, we apply division lemma to 90 and 332, to get

332 = 90 x 3 + 62

Step 3: We consider the new divisor 90 and the new remainder 62, and apply the division lemma to get

90 = 62 x 1 + 28

We consider the new divisor 62 and the new remainder 28,and apply the division lemma to get

62 = 28 x 2 + 6

We consider the new divisor 28 and the new remainder 6,and apply the division lemma to get

28 = 6 x 4 + 4

We consider the new divisor 6 and the new remainder 4,and apply the division lemma to get

6 = 4 x 1 + 2

We consider the new divisor 4 and the new remainder 2,and apply the division lemma to get

4 = 2 x 2 + 0

The remainder has now become zero, so our procedure stops. Since the divisor at this stage is 2, the HCF of 754 and 332 is 2

Notice that 2 = HCF(4,2) = HCF(6,4) = HCF(28,6) = HCF(62,28) = HCF(90,62) = HCF(332,90) = HCF(754,332) .

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

Step 1: Since 724 > 2, we apply the division lemma to 724 and 2, to get

724 = 2 x 362 + 0

The remainder has now become zero, so our procedure stops. Since the divisor at this stage is 2, the HCF of 2 and 724 is 2

Notice that 2 = HCF(724,2) .

HCF using Euclid's Algorithm Calculation Examples

Here are some samples of HCF using Euclid's Algorithm calculations.

Frequently Asked Questions on HCF of 754, 332, 724 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 754, 332, 724?

Answer: HCF of 754, 332, 724 is 2 the largest number that divides all the numbers leaving a remainder zero.

3. How to find HCF of 754, 332, 724 using Euclid's Algorithm?

Answer: For arbitrary numbers 754, 332, 724 apply Euclid’s Division Lemma in succession until you obtain a remainder zero. HCF is the remainder in the last but one step.