Highest Common Factor of 735, 454, 712 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 735, 454, 712 i.e. 1 the largest integer that leaves a remainder zero for all numbers.

HCF of 735, 454, 712 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 735, 454, 712 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 735, 454, 712 is 1.

HCF(735, 454, 712) = 1

HCF of 735, 454, 712 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 735, 454, 712 is 1.

Highest Common Factor of 735,454,712 using Euclid's algorithm

Highest Common Factor of 735,454,712 is 1

Step 1: Since 735 > 454, we apply the division lemma to 735 and 454, to get

735 = 454 x 1 + 281

Step 2: Since the reminder 454 ≠ 0, we apply division lemma to 281 and 454, to get

454 = 281 x 1 + 173

Step 3: We consider the new divisor 281 and the new remainder 173, and apply the division lemma to get

281 = 173 x 1 + 108

We consider the new divisor 173 and the new remainder 108,and apply the division lemma to get

173 = 108 x 1 + 65

We consider the new divisor 108 and the new remainder 65,and apply the division lemma to get

108 = 65 x 1 + 43

We consider the new divisor 65 and the new remainder 43,and apply the division lemma to get

65 = 43 x 1 + 22

We consider the new divisor 43 and the new remainder 22,and apply the division lemma to get

43 = 22 x 1 + 21

We consider the new divisor 22 and the new remainder 21,and apply the division lemma to get

22 = 21 x 1 + 1

We consider the new divisor 21 and the new remainder 1,and apply the division lemma to get

21 = 1 x 21 + 0

The remainder has now become zero, so our procedure stops. Since the divisor at this stage is 1, the HCF of 735 and 454 is 1

Notice that 1 = HCF(21,1) = HCF(22,21) = HCF(43,22) = HCF(65,43) = HCF(108,65) = HCF(173,108) = HCF(281,173) = HCF(454,281) = HCF(735,454) .

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

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

712 = 1 x 712 + 0

The remainder has now become zero, so our procedure stops. Since the divisor at this stage is 1, the HCF of 1 and 712 is 1

Notice that 1 = HCF(712,1) .

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Frequently Asked Questions on HCF of 735, 454, 712 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 735, 454, 712?

Answer: HCF of 735, 454, 712 is 1 the largest number that divides all the numbers leaving a remainder zero.

3. How to find HCF of 735, 454, 712 using Euclid's Algorithm?

Answer: For arbitrary numbers 735, 454, 712 apply Euclid’s Division Lemma in succession until you obtain a remainder zero. HCF is the remainder in the last but one step.