Highest Common Factor of 659, 996, 51 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 659, 996, 51 i.e. 1 the largest integer that leaves a remainder zero for all numbers.

HCF of 659, 996, 51 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 659, 996, 51 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 659, 996, 51 is 1.

HCF(659, 996, 51) = 1

HCF of 659, 996, 51 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 659, 996, 51 is 1.

Highest Common Factor of 659,996,51 using Euclid's algorithm

Highest Common Factor of 659,996,51 is 1

Step 1: Since 996 > 659, we apply the division lemma to 996 and 659, to get

996 = 659 x 1 + 337

Step 2: Since the reminder 659 ≠ 0, we apply division lemma to 337 and 659, to get

659 = 337 x 1 + 322

Step 3: We consider the new divisor 337 and the new remainder 322, and apply the division lemma to get

337 = 322 x 1 + 15

We consider the new divisor 322 and the new remainder 15,and apply the division lemma to get

322 = 15 x 21 + 7

We consider the new divisor 15 and the new remainder 7,and apply the division lemma to get

15 = 7 x 2 + 1

We consider the new divisor 7 and the new remainder 1,and apply the division lemma to get

7 = 1 x 7 + 0

The remainder has now become zero, so our procedure stops. Since the divisor at this stage is 1, the HCF of 659 and 996 is 1

Notice that 1 = HCF(7,1) = HCF(15,7) = HCF(322,15) = HCF(337,322) = HCF(659,337) = HCF(996,659) .

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

Step 1: Since 51 > 1, we apply the division lemma to 51 and 1, to get

51 = 1 x 51 + 0

The remainder has now become zero, so our procedure stops. Since the divisor at this stage is 1, the HCF of 1 and 51 is 1

Notice that 1 = HCF(51,1) .

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Frequently Asked Questions on HCF of 659, 996, 51 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 659, 996, 51?

Answer: HCF of 659, 996, 51 is 1 the largest number that divides all the numbers leaving a remainder zero.

3. How to find HCF of 659, 996, 51 using Euclid's Algorithm?

Answer: For arbitrary numbers 659, 996, 51 apply Euclid’s Division Lemma in succession until you obtain a remainder zero. HCF is the remainder in the last but one step.