Highest Common Factor of 870, 365, 693 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 870, 365, 693 i.e. 1 the largest integer that leaves a remainder zero for all numbers.

HCF of 870, 365, 693 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 870, 365, 693 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 870, 365, 693 is 1.

HCF(870, 365, 693) = 1

HCF of 870, 365, 693 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 870, 365, 693 is 1.

Highest Common Factor of 870,365,693 using Euclid's algorithm

Highest Common Factor of 870,365,693 is 1

Step 1: Since 870 > 365, we apply the division lemma to 870 and 365, to get

870 = 365 x 2 + 140

Step 2: Since the reminder 365 ≠ 0, we apply division lemma to 140 and 365, to get

365 = 140 x 2 + 85

Step 3: We consider the new divisor 140 and the new remainder 85, and apply the division lemma to get

140 = 85 x 1 + 55

We consider the new divisor 85 and the new remainder 55,and apply the division lemma to get

85 = 55 x 1 + 30

We consider the new divisor 55 and the new remainder 30,and apply the division lemma to get

55 = 30 x 1 + 25

We consider the new divisor 30 and the new remainder 25,and apply the division lemma to get

30 = 25 x 1 + 5

We consider the new divisor 25 and the new remainder 5,and apply the division lemma to get

25 = 5 x 5 + 0

The remainder has now become zero, so our procedure stops. Since the divisor at this stage is 5, the HCF of 870 and 365 is 5

Notice that 5 = HCF(25,5) = HCF(30,25) = HCF(55,30) = HCF(85,55) = HCF(140,85) = HCF(365,140) = HCF(870,365) .

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

Step 1: Since 693 > 5, we apply the division lemma to 693 and 5, to get

693 = 5 x 138 + 3

Step 2: Since the reminder 5 ≠ 0, we apply division lemma to 3 and 5, to get

5 = 3 x 1 + 2

Step 3: 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 5 and 693 is 1

Notice that 1 = HCF(2,1) = HCF(3,2) = HCF(5,3) = HCF(693,5) .

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Frequently Asked Questions on HCF of 870, 365, 693 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 870, 365, 693?

Answer: HCF of 870, 365, 693 is 1 the largest number that divides all the numbers leaving a remainder zero.

3. How to find HCF of 870, 365, 693 using Euclid's Algorithm?

Answer: For arbitrary numbers 870, 365, 693 apply Euclid’s Division Lemma in succession until you obtain a remainder zero. HCF is the remainder in the last but one step.