Highest Common Factor of 827, 652 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 827, 652 i.e. 1 the largest integer that leaves a remainder zero for all numbers.

HCF of 827, 652 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 827, 652 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 827, 652 is 1.

HCF(827, 652) = 1

HCF of 827, 652 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 827, 652 is 1.

Highest Common Factor of 827,652 using Euclid's algorithm

Highest Common Factor of 827,652 is 1

Step 1: Since 827 > 652, we apply the division lemma to 827 and 652, to get

827 = 652 x 1 + 175

Step 2: Since the reminder 652 ≠ 0, we apply division lemma to 175 and 652, to get

652 = 175 x 3 + 127

Step 3: We consider the new divisor 175 and the new remainder 127, and apply the division lemma to get

175 = 127 x 1 + 48

We consider the new divisor 127 and the new remainder 48,and apply the division lemma to get

127 = 48 x 2 + 31

We consider the new divisor 48 and the new remainder 31,and apply the division lemma to get

48 = 31 x 1 + 17

We consider the new divisor 31 and the new remainder 17,and apply the division lemma to get

31 = 17 x 1 + 14

We consider the new divisor 17 and the new remainder 14,and apply the division lemma to get

17 = 14 x 1 + 3

We consider the new divisor 14 and the new remainder 3,and apply the division lemma to get

14 = 3 x 4 + 2

We consider the new divisor 3 and the new remainder 2,and apply the division lemma to get

3 = 2 x 1 + 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 827 and 652 is 1

Notice that 1 = HCF(2,1) = HCF(3,2) = HCF(14,3) = HCF(17,14) = HCF(31,17) = HCF(48,31) = HCF(127,48) = HCF(175,127) = HCF(652,175) = HCF(827,652) .

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Frequently Asked Questions on HCF of 827, 652 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 827, 652?

Answer: HCF of 827, 652 is 1 the largest number that divides all the numbers leaving a remainder zero.

3. How to find HCF of 827, 652 using Euclid's Algorithm?

Answer: For arbitrary numbers 827, 652 apply Euclid’s Division Lemma in succession until you obtain a remainder zero. HCF is the remainder in the last but one step.