Highest Common Factor of 516, 898, 39 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 516, 898, 39 i.e. 1 the largest integer that leaves a remainder zero for all numbers.

HCF of 516, 898, 39 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 516, 898, 39 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 516, 898, 39 is 1.

HCF(516, 898, 39) = 1

HCF of 516, 898, 39 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 516, 898, 39 is 1.

Highest Common Factor of 516,898,39 using Euclid's algorithm

Highest Common Factor of 516,898,39 is 1

Step 1: Since 898 > 516, we apply the division lemma to 898 and 516, to get

898 = 516 x 1 + 382

Step 2: Since the reminder 516 ≠ 0, we apply division lemma to 382 and 516, to get

516 = 382 x 1 + 134

Step 3: We consider the new divisor 382 and the new remainder 134, and apply the division lemma to get

382 = 134 x 2 + 114

We consider the new divisor 134 and the new remainder 114,and apply the division lemma to get

134 = 114 x 1 + 20

We consider the new divisor 114 and the new remainder 20,and apply the division lemma to get

114 = 20 x 5 + 14

We consider the new divisor 20 and the new remainder 14,and apply the division lemma to get

20 = 14 x 1 + 6

We consider the new divisor 14 and the new remainder 6,and apply the division lemma to get

14 = 6 x 2 + 2

We consider the new divisor 6 and the new remainder 2,and apply the division lemma to get

6 = 2 x 3 + 0

The remainder has now become zero, so our procedure stops. Since the divisor at this stage is 2, the HCF of 516 and 898 is 2

Notice that 2 = HCF(6,2) = HCF(14,6) = HCF(20,14) = HCF(114,20) = HCF(134,114) = HCF(382,134) = HCF(516,382) = HCF(898,516) .

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

Step 1: Since 39 > 2, we apply the division lemma to 39 and 2, to get

39 = 2 x 19 + 1

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

2 = 1 x 2 + 0

The remainder has now become zero, so our procedure stops. Since the divisor at this stage is 1, the HCF of 2 and 39 is 1

Notice that 1 = HCF(2,1) = HCF(39,2) .

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Frequently Asked Questions on HCF of 516, 898, 39 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 516, 898, 39?

Answer: HCF of 516, 898, 39 is 1 the largest number that divides all the numbers leaving a remainder zero.

3. How to find HCF of 516, 898, 39 using Euclid's Algorithm?

Answer: For arbitrary numbers 516, 898, 39 apply Euclid’s Division Lemma in succession until you obtain a remainder zero. HCF is the remainder in the last but one step.