Highest Common Factor of 852, 516, 913 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 852, 516, 913 i.e. 1 the largest integer that leaves a remainder zero for all numbers.

HCF of 852, 516, 913 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 852, 516, 913 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 852, 516, 913 is 1.

HCF(852, 516, 913) = 1

HCF of 852, 516, 913 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 852, 516, 913 is 1.

Highest Common Factor of 852,516,913 using Euclid's algorithm

Highest Common Factor of 852,516,913 is 1

Step 1: Since 852 > 516, we apply the division lemma to 852 and 516, to get

852 = 516 x 1 + 336

Step 2: Since the reminder 516 ≠ 0, we apply division lemma to 336 and 516, to get

516 = 336 x 1 + 180

Step 3: We consider the new divisor 336 and the new remainder 180, and apply the division lemma to get

336 = 180 x 1 + 156

We consider the new divisor 180 and the new remainder 156,and apply the division lemma to get

180 = 156 x 1 + 24

We consider the new divisor 156 and the new remainder 24,and apply the division lemma to get

156 = 24 x 6 + 12

We consider the new divisor 24 and the new remainder 12,and apply the division lemma to get

24 = 12 x 2 + 0

The remainder has now become zero, so our procedure stops. Since the divisor at this stage is 12, the HCF of 852 and 516 is 12

Notice that 12 = HCF(24,12) = HCF(156,24) = HCF(180,156) = HCF(336,180) = HCF(516,336) = HCF(852,516) .

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

Step 1: Since 913 > 12, we apply the division lemma to 913 and 12, to get

913 = 12 x 76 + 1

Step 2: Since the reminder 12 ≠ 0, we apply division lemma to 1 and 12, to get

12 = 1 x 12 + 0

The remainder has now become zero, so our procedure stops. Since the divisor at this stage is 1, the HCF of 12 and 913 is 1

Notice that 1 = HCF(12,1) = HCF(913,12) .

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Frequently Asked Questions on HCF of 852, 516, 913 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 852, 516, 913?

Answer: HCF of 852, 516, 913 is 1 the largest number that divides all the numbers leaving a remainder zero.

3. How to find HCF of 852, 516, 913 using Euclid's Algorithm?

Answer: For arbitrary numbers 852, 516, 913 apply Euclid’s Division Lemma in succession until you obtain a remainder zero. HCF is the remainder in the last but one step.