Highest Common Factor of 837, 659, 513, 14 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 837, 659, 513, 14 i.e. 1 the largest integer that leaves a remainder zero for all numbers.

HCF of 837, 659, 513, 14 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 837, 659, 513, 14 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 837, 659, 513, 14 is 1.

HCF(837, 659, 513, 14) = 1

HCF of 837, 659, 513, 14 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 837, 659, 513, 14 is 1.

Highest Common Factor of 837,659,513,14 using Euclid's algorithm

Highest Common Factor of 837,659,513,14 is 1

Step 1: Since 837 > 659, we apply the division lemma to 837 and 659, to get

837 = 659 x 1 + 178

Step 2: Since the reminder 659 ≠ 0, we apply division lemma to 178 and 659, to get

659 = 178 x 3 + 125

Step 3: We consider the new divisor 178 and the new remainder 125, and apply the division lemma to get

178 = 125 x 1 + 53

We consider the new divisor 125 and the new remainder 53,and apply the division lemma to get

125 = 53 x 2 + 19

We consider the new divisor 53 and the new remainder 19,and apply the division lemma to get

53 = 19 x 2 + 15

We consider the new divisor 19 and the new remainder 15,and apply the division lemma to get

19 = 15 x 1 + 4

We consider the new divisor 15 and the new remainder 4,and apply the division lemma to get

15 = 4 x 3 + 3

We consider the new divisor 4 and the new remainder 3,and apply the division lemma to get

4 = 3 x 1 + 1

We consider the new divisor 3 and the new remainder 1,and apply the division lemma 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 837 and 659 is 1

Notice that 1 = HCF(3,1) = HCF(4,3) = HCF(15,4) = HCF(19,15) = HCF(53,19) = HCF(125,53) = HCF(178,125) = HCF(659,178) = HCF(837,659) .

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

Step 1: Since 513 > 1, we apply the division lemma to 513 and 1, to get

513 = 1 x 513 + 0

The remainder has now become zero, so our procedure stops. Since the divisor at this stage is 1, the HCF of 1 and 513 is 1

Notice that 1 = HCF(513,1) .

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

Step 1: Since 14 > 1, we apply the division lemma to 14 and 1, to get

14 = 1 x 14 + 0

The remainder has now become zero, so our procedure stops. Since the divisor at this stage is 1, the HCF of 1 and 14 is 1

Notice that 1 = HCF(14,1) .

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Frequently Asked Questions on HCF of 837, 659, 513, 14 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 837, 659, 513, 14?

Answer: HCF of 837, 659, 513, 14 is 1 the largest number that divides all the numbers leaving a remainder zero.

3. How to find HCF of 837, 659, 513, 14 using Euclid's Algorithm?

Answer: For arbitrary numbers 837, 659, 513, 14 apply Euclid’s Division Lemma in succession until you obtain a remainder zero. HCF is the remainder in the last but one step.