Highest Common Factor of 744, 897, 872 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 744, 897, 872 i.e. 1 the largest integer that leaves a remainder zero for all numbers.

HCF of 744, 897, 872 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 744, 897, 872 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 744, 897, 872 is 1.

HCF(744, 897, 872) = 1

HCF of 744, 897, 872 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 744, 897, 872 is 1.

Highest Common Factor of 744,897,872 using Euclid's algorithm

Highest Common Factor of 744,897,872 is 1

Step 1: Since 897 > 744, we apply the division lemma to 897 and 744, to get

897 = 744 x 1 + 153

Step 2: Since the reminder 744 ≠ 0, we apply division lemma to 153 and 744, to get

744 = 153 x 4 + 132

Step 3: We consider the new divisor 153 and the new remainder 132, and apply the division lemma to get

153 = 132 x 1 + 21

We consider the new divisor 132 and the new remainder 21,and apply the division lemma to get

132 = 21 x 6 + 6

We consider the new divisor 21 and the new remainder 6,and apply the division lemma to get

21 = 6 x 3 + 3

We consider the new divisor 6 and the new remainder 3,and apply the division lemma to get

6 = 3 x 2 + 0

The remainder has now become zero, so our procedure stops. Since the divisor at this stage is 3, the HCF of 744 and 897 is 3

Notice that 3 = HCF(6,3) = HCF(21,6) = HCF(132,21) = HCF(153,132) = HCF(744,153) = HCF(897,744) .

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

Step 1: Since 872 > 3, we apply the division lemma to 872 and 3, to get

872 = 3 x 290 + 2

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

3 = 2 x 1 + 1

Step 3: 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 3 and 872 is 1

Notice that 1 = HCF(2,1) = HCF(3,2) = HCF(872,3) .

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Frequently Asked Questions on HCF of 744, 897, 872 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 744, 897, 872?

Answer: HCF of 744, 897, 872 is 1 the largest number that divides all the numbers leaving a remainder zero.

3. How to find HCF of 744, 897, 872 using Euclid's Algorithm?

Answer: For arbitrary numbers 744, 897, 872 apply Euclid’s Division Lemma in succession until you obtain a remainder zero. HCF is the remainder in the last but one step.