Highest Common Factor of 432, 744, 764 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 432, 744, 764 i.e. 4 the largest integer that leaves a remainder zero for all numbers.

HCF of 432, 744, 764 is 4 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 432, 744, 764 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 432, 744, 764 is 4.

HCF(432, 744, 764) = 4

HCF of 432, 744, 764 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 432, 744, 764 is 4.

Highest Common Factor of 432,744,764 using Euclid's algorithm

Highest Common Factor of 432,744,764 is 4

Step 1: Since 744 > 432, we apply the division lemma to 744 and 432, to get

744 = 432 x 1 + 312

Step 2: Since the reminder 432 ≠ 0, we apply division lemma to 312 and 432, to get

432 = 312 x 1 + 120

Step 3: We consider the new divisor 312 and the new remainder 120, and apply the division lemma to get

312 = 120 x 2 + 72

We consider the new divisor 120 and the new remainder 72,and apply the division lemma to get

120 = 72 x 1 + 48

We consider the new divisor 72 and the new remainder 48,and apply the division lemma to get

72 = 48 x 1 + 24

We consider the new divisor 48 and the new remainder 24,and apply the division lemma to get

48 = 24 x 2 + 0

The remainder has now become zero, so our procedure stops. Since the divisor at this stage is 24, the HCF of 432 and 744 is 24

Notice that 24 = HCF(48,24) = HCF(72,48) = HCF(120,72) = HCF(312,120) = HCF(432,312) = HCF(744,432) .

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

Step 1: Since 764 > 24, we apply the division lemma to 764 and 24, to get

764 = 24 x 31 + 20

Step 2: Since the reminder 24 ≠ 0, we apply division lemma to 20 and 24, to get

24 = 20 x 1 + 4

Step 3: We consider the new divisor 20 and the new remainder 4, and apply the division lemma to get

20 = 4 x 5 + 0

The remainder has now become zero, so our procedure stops. Since the divisor at this stage is 4, the HCF of 24 and 764 is 4

Notice that 4 = HCF(20,4) = HCF(24,20) = HCF(764,24) .

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Frequently Asked Questions on HCF of 432, 744, 764 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 432, 744, 764?

Answer: HCF of 432, 744, 764 is 4 the largest number that divides all the numbers leaving a remainder zero.

3. How to find HCF of 432, 744, 764 using Euclid's Algorithm?

Answer: For arbitrary numbers 432, 744, 764 apply Euclid’s Division Lemma in succession until you obtain a remainder zero. HCF is the remainder in the last but one step.