Highest Common Factor of 432, 712, 772 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, 712, 772 i.e. 4 the largest integer that leaves a remainder zero for all numbers.

HCF of 432, 712, 772 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, 712, 772 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, 712, 772 is 4.

HCF(432, 712, 772) = 4

HCF of 432, 712, 772 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, 712, 772 is 4.

Highest Common Factor of 432,712,772 using Euclid's algorithm

Highest Common Factor of 432,712,772 is 4

Step 1: Since 712 > 432, we apply the division lemma to 712 and 432, to get

712 = 432 x 1 + 280

Step 2: Since the reminder 432 ≠ 0, we apply division lemma to 280 and 432, to get

432 = 280 x 1 + 152

Step 3: We consider the new divisor 280 and the new remainder 152, and apply the division lemma to get

280 = 152 x 1 + 128

We consider the new divisor 152 and the new remainder 128,and apply the division lemma to get

152 = 128 x 1 + 24

We consider the new divisor 128 and the new remainder 24,and apply the division lemma to get

128 = 24 x 5 + 8

We consider the new divisor 24 and the new remainder 8,and apply the division lemma to get

24 = 8 x 3 + 0

The remainder has now become zero, so our procedure stops. Since the divisor at this stage is 8, the HCF of 432 and 712 is 8

Notice that 8 = HCF(24,8) = HCF(128,24) = HCF(152,128) = HCF(280,152) = HCF(432,280) = HCF(712,432) .

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

Step 1: Since 772 > 8, we apply the division lemma to 772 and 8, to get

772 = 8 x 96 + 4

Step 2: Since the reminder 8 ≠ 0, we apply division lemma to 4 and 8, to get

8 = 4 x 2 + 0

The remainder has now become zero, so our procedure stops. Since the divisor at this stage is 4, the HCF of 8 and 772 is 4

Notice that 4 = HCF(8,4) = HCF(772,8) .

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Frequently Asked Questions on HCF of 432, 712, 772 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, 712, 772?

Answer: HCF of 432, 712, 772 is 4 the largest number that divides all the numbers leaving a remainder zero.

3. How to find HCF of 432, 712, 772 using Euclid's Algorithm?

Answer: For arbitrary numbers 432, 712, 772 apply Euclid’s Division Lemma in succession until you obtain a remainder zero. HCF is the remainder in the last but one step.