Highest Common Factor of 860, 165, 728, 782 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 860, 165, 728, 782 i.e. 1 the largest integer that leaves a remainder zero for all numbers.

HCF of 860, 165, 728, 782 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 860, 165, 728, 782 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 860, 165, 728, 782 is 1.

HCF(860, 165, 728, 782) = 1

HCF of 860, 165, 728, 782 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 860, 165, 728, 782 is 1.

Highest Common Factor of 860,165,728,782 using Euclid's algorithm

Highest Common Factor of 860,165,728,782 is 1

Step 1: Since 860 > 165, we apply the division lemma to 860 and 165, to get

860 = 165 x 5 + 35

Step 2: Since the reminder 165 ≠ 0, we apply division lemma to 35 and 165, to get

165 = 35 x 4 + 25

Step 3: We consider the new divisor 35 and the new remainder 25, and apply the division lemma to get

35 = 25 x 1 + 10

We consider the new divisor 25 and the new remainder 10,and apply the division lemma to get

25 = 10 x 2 + 5

We consider the new divisor 10 and the new remainder 5,and apply the division lemma to get

10 = 5 x 2 + 0

The remainder has now become zero, so our procedure stops. Since the divisor at this stage is 5, the HCF of 860 and 165 is 5

Notice that 5 = HCF(10,5) = HCF(25,10) = HCF(35,25) = HCF(165,35) = HCF(860,165) .

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

Step 1: Since 728 > 5, we apply the division lemma to 728 and 5, to get

728 = 5 x 145 + 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 728 is 1

Notice that 1 = HCF(2,1) = HCF(3,2) = HCF(5,3) = HCF(728,5) .

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

Step 1: Since 782 > 1, we apply the division lemma to 782 and 1, to get

782 = 1 x 782 + 0

The remainder has now become zero, so our procedure stops. Since the divisor at this stage is 1, the HCF of 1 and 782 is 1

Notice that 1 = HCF(782,1) .

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Frequently Asked Questions on HCF of 860, 165, 728, 782 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 860, 165, 728, 782?

Answer: HCF of 860, 165, 728, 782 is 1 the largest number that divides all the numbers leaving a remainder zero.

3. How to find HCF of 860, 165, 728, 782 using Euclid's Algorithm?

Answer: For arbitrary numbers 860, 165, 728, 782 apply Euclid’s Division Lemma in succession until you obtain a remainder zero. HCF is the remainder in the last but one step.