Highest Common Factor of 877, 1591, 8270 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 877, 1591, 8270 i.e. 1 the largest integer that leaves a remainder zero for all numbers.

HCF of 877, 1591, 8270 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 877, 1591, 8270 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 877, 1591, 8270 is 1.

HCF(877, 1591, 8270) = 1

HCF of 877, 1591, 8270 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 877, 1591, 8270 is 1.

Highest Common Factor of 877,1591,8270 using Euclid's algorithm

Highest Common Factor of 877,1591,8270 is 1

Step 1: Since 1591 > 877, we apply the division lemma to 1591 and 877, to get

1591 = 877 x 1 + 714

Step 2: Since the reminder 877 ≠ 0, we apply division lemma to 714 and 877, to get

877 = 714 x 1 + 163

Step 3: We consider the new divisor 714 and the new remainder 163, and apply the division lemma to get

714 = 163 x 4 + 62

We consider the new divisor 163 and the new remainder 62,and apply the division lemma to get

163 = 62 x 2 + 39

We consider the new divisor 62 and the new remainder 39,and apply the division lemma to get

62 = 39 x 1 + 23

We consider the new divisor 39 and the new remainder 23,and apply the division lemma to get

39 = 23 x 1 + 16

We consider the new divisor 23 and the new remainder 16,and apply the division lemma to get

23 = 16 x 1 + 7

We consider the new divisor 16 and the new remainder 7,and apply the division lemma to get

16 = 7 x 2 + 2

We consider the new divisor 7 and the new remainder 2,and apply the division lemma to get

7 = 2 x 3 + 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 877 and 1591 is 1

Notice that 1 = HCF(2,1) = HCF(7,2) = HCF(16,7) = HCF(23,16) = HCF(39,23) = HCF(62,39) = HCF(163,62) = HCF(714,163) = HCF(877,714) = HCF(1591,877) .

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

Step 1: Since 8270 > 1, we apply the division lemma to 8270 and 1, to get

8270 = 1 x 8270 + 0

The remainder has now become zero, so our procedure stops. Since the divisor at this stage is 1, the HCF of 1 and 8270 is 1

Notice that 1 = HCF(8270,1) .

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Frequently Asked Questions on HCF of 877, 1591, 8270 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 877, 1591, 8270?

Answer: HCF of 877, 1591, 8270 is 1 the largest number that divides all the numbers leaving a remainder zero.

3. How to find HCF of 877, 1591, 8270 using Euclid's Algorithm?

Answer: For arbitrary numbers 877, 1591, 8270 apply Euclid’s Division Lemma in succession until you obtain a remainder zero. HCF is the remainder in the last but one step.