Highest Common Factor of 936, 659 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 936, 659 i.e. 1 the largest integer that leaves a remainder zero for all numbers.

HCF of 936, 659 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 936, 659 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 936, 659 is 1.

HCF(936, 659) = 1

HCF of 936, 659 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 936, 659 is 1.

Highest Common Factor of 936,659 using Euclid's algorithm

Highest Common Factor of 936,659 is 1

Step 1: Since 936 > 659, we apply the division lemma to 936 and 659, to get

936 = 659 x 1 + 277

Step 2: Since the reminder 659 ≠ 0, we apply division lemma to 277 and 659, to get

659 = 277 x 2 + 105

Step 3: We consider the new divisor 277 and the new remainder 105, and apply the division lemma to get

277 = 105 x 2 + 67

We consider the new divisor 105 and the new remainder 67,and apply the division lemma to get

105 = 67 x 1 + 38

We consider the new divisor 67 and the new remainder 38,and apply the division lemma to get

67 = 38 x 1 + 29

We consider the new divisor 38 and the new remainder 29,and apply the division lemma to get

38 = 29 x 1 + 9

We consider the new divisor 29 and the new remainder 9,and apply the division lemma to get

29 = 9 x 3 + 2

We consider the new divisor 9 and the new remainder 2,and apply the division lemma to get

9 = 2 x 4 + 1

We consider the new divisor 2 and the new remainder 1,and apply the division lemma 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 936 and 659 is 1

Notice that 1 = HCF(2,1) = HCF(9,2) = HCF(29,9) = HCF(38,29) = HCF(67,38) = HCF(105,67) = HCF(277,105) = HCF(659,277) = HCF(936,659) .

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Frequently Asked Questions on HCF of 936, 659 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 936, 659?

Answer: HCF of 936, 659 is 1 the largest number that divides all the numbers leaving a remainder zero.

3. How to find HCF of 936, 659 using Euclid's Algorithm?

Answer: For arbitrary numbers 936, 659 apply Euclid’s Division Lemma in succession until you obtain a remainder zero. HCF is the remainder in the last but one step.