Highest Common Factor of 738, 291, 634 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 738, 291, 634 i.e. 1 the largest integer that leaves a remainder zero for all numbers.

HCF of 738, 291, 634 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 738, 291, 634 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 738, 291, 634 is 1.

HCF(738, 291, 634) = 1

HCF of 738, 291, 634 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 738, 291, 634 is 1.

Highest Common Factor of 738,291,634 using Euclid's algorithm

Highest Common Factor of 738,291,634 is 1

Step 1: Since 738 > 291, we apply the division lemma to 738 and 291, to get

738 = 291 x 2 + 156

Step 2: Since the reminder 291 ≠ 0, we apply division lemma to 156 and 291, to get

291 = 156 x 1 + 135

Step 3: We consider the new divisor 156 and the new remainder 135, and apply the division lemma to get

156 = 135 x 1 + 21

We consider the new divisor 135 and the new remainder 21,and apply the division lemma to get

135 = 21 x 6 + 9

We consider the new divisor 21 and the new remainder 9,and apply the division lemma to get

21 = 9 x 2 + 3

We consider the new divisor 9 and the new remainder 3,and apply the division lemma to get

9 = 3 x 3 + 0

The remainder has now become zero, so our procedure stops. Since the divisor at this stage is 3, the HCF of 738 and 291 is 3

Notice that 3 = HCF(9,3) = HCF(21,9) = HCF(135,21) = HCF(156,135) = HCF(291,156) = HCF(738,291) .

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

Step 1: Since 634 > 3, we apply the division lemma to 634 and 3, to get

634 = 3 x 211 + 1

Step 2: Since the reminder 3 ≠ 0, we apply division lemma to 1 and 3, to get

3 = 1 x 3 + 0

The remainder has now become zero, so our procedure stops. Since the divisor at this stage is 1, the HCF of 3 and 634 is 1

Notice that 1 = HCF(3,1) = HCF(634,3) .

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Frequently Asked Questions on HCF of 738, 291, 634 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 738, 291, 634?

Answer: HCF of 738, 291, 634 is 1 the largest number that divides all the numbers leaving a remainder zero.

3. How to find HCF of 738, 291, 634 using Euclid's Algorithm?

Answer: For arbitrary numbers 738, 291, 634 apply Euclid’s Division Lemma in succession until you obtain a remainder zero. HCF is the remainder in the last but one step.