Highest Common Factor of 734, 572, 652 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 734, 572, 652 i.e. 2 the largest integer that leaves a remainder zero for all numbers.

HCF of 734, 572, 652 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 734, 572, 652 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 734, 572, 652 is 2.

HCF(734, 572, 652) = 2

HCF of 734, 572, 652 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 734, 572, 652 is 2.

Highest Common Factor of 734,572,652 using Euclid's algorithm

Highest Common Factor of 734,572,652 is 2

Step 1: Since 734 > 572, we apply the division lemma to 734 and 572, to get

734 = 572 x 1 + 162

Step 2: Since the reminder 572 ≠ 0, we apply division lemma to 162 and 572, to get

572 = 162 x 3 + 86

Step 3: We consider the new divisor 162 and the new remainder 86, and apply the division lemma to get

162 = 86 x 1 + 76

We consider the new divisor 86 and the new remainder 76,and apply the division lemma to get

86 = 76 x 1 + 10

We consider the new divisor 76 and the new remainder 10,and apply the division lemma to get

76 = 10 x 7 + 6

We consider the new divisor 10 and the new remainder 6,and apply the division lemma to get

10 = 6 x 1 + 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 734 and 572 is 2

Notice that 2 = HCF(4,2) = HCF(6,4) = HCF(10,6) = HCF(76,10) = HCF(86,76) = HCF(162,86) = HCF(572,162) = HCF(734,572) .

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

Step 1: Since 652 > 2, we apply the division lemma to 652 and 2, to get

652 = 2 x 326 + 0

The remainder has now become zero, so our procedure stops. Since the divisor at this stage is 2, the HCF of 2 and 652 is 2

Notice that 2 = HCF(652,2) .

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Frequently Asked Questions on HCF of 734, 572, 652 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 734, 572, 652?

Answer: HCF of 734, 572, 652 is 2 the largest number that divides all the numbers leaving a remainder zero.

3. How to find HCF of 734, 572, 652 using Euclid's Algorithm?

Answer: For arbitrary numbers 734, 572, 652 apply Euclid’s Division Lemma in succession until you obtain a remainder zero. HCF is the remainder in the last but one step.