Highest Common Factor of 780, 3634, 2152 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 780, 3634, 2152 i.e. 2 the largest integer that leaves a remainder zero for all numbers.

HCF of 780, 3634, 2152 is 2 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 780, 3634, 2152 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 780, 3634, 2152 is 2.

HCF(780, 3634, 2152) = 2

HCF of 780, 3634, 2152 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 780, 3634, 2152 is 2.

Highest Common Factor of 780,3634,2152 using Euclid's algorithm

Highest Common Factor of 780,3634,2152 is 2

Step 1: Since 3634 > 780, we apply the division lemma to 3634 and 780, to get

3634 = 780 x 4 + 514

Step 2: Since the reminder 780 ≠ 0, we apply division lemma to 514 and 780, to get

780 = 514 x 1 + 266

Step 3: We consider the new divisor 514 and the new remainder 266, and apply the division lemma to get

514 = 266 x 1 + 248

We consider the new divisor 266 and the new remainder 248,and apply the division lemma to get

266 = 248 x 1 + 18

We consider the new divisor 248 and the new remainder 18,and apply the division lemma to get

248 = 18 x 13 + 14

We consider the new divisor 18 and the new remainder 14,and apply the division lemma to get

18 = 14 x 1 + 4

We consider the new divisor 14 and the new remainder 4,and apply the division lemma to get

14 = 4 x 3 + 2

We consider the new divisor 4 and the new remainder 2,and apply the division lemma to get

4 = 2 x 2 + 0

The remainder has now become zero, so our procedure stops. Since the divisor at this stage is 2, the HCF of 780 and 3634 is 2

Notice that 2 = HCF(4,2) = HCF(14,4) = HCF(18,14) = HCF(248,18) = HCF(266,248) = HCF(514,266) = HCF(780,514) = HCF(3634,780) .

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

Step 1: Since 2152 > 2, we apply the division lemma to 2152 and 2, to get

2152 = 2 x 1076 + 0

The remainder has now become zero, so our procedure stops. Since the divisor at this stage is 2, the HCF of 2 and 2152 is 2

Notice that 2 = HCF(2152,2) .

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Frequently Asked Questions on HCF of 780, 3634, 2152 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 780, 3634, 2152?

Answer: HCF of 780, 3634, 2152 is 2 the largest number that divides all the numbers leaving a remainder zero.

3. How to find HCF of 780, 3634, 2152 using Euclid's Algorithm?

Answer: For arbitrary numbers 780, 3634, 2152 apply Euclid’s Division Lemma in succession until you obtain a remainder zero. HCF is the remainder in the last but one step.