Highest Common Factor of 320, 867, 60 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 320, 867, 60 i.e. 1 the largest integer that leaves a remainder zero for all numbers.

HCF of 320, 867, 60 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 320, 867, 60 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 320, 867, 60 is 1.

HCF(320, 867, 60) = 1

HCF of 320, 867, 60 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 320, 867, 60 is 1.

Highest Common Factor of 320,867,60 using Euclid's algorithm

Highest Common Factor of 320,867,60 is 1

Step 1: Since 867 > 320, we apply the division lemma to 867 and 320, to get

867 = 320 x 2 + 227

Step 2: Since the reminder 320 ≠ 0, we apply division lemma to 227 and 320, to get

320 = 227 x 1 + 93

Step 3: We consider the new divisor 227 and the new remainder 93, and apply the division lemma to get

227 = 93 x 2 + 41

We consider the new divisor 93 and the new remainder 41,and apply the division lemma to get

93 = 41 x 2 + 11

We consider the new divisor 41 and the new remainder 11,and apply the division lemma to get

41 = 11 x 3 + 8

We consider the new divisor 11 and the new remainder 8,and apply the division lemma to get

11 = 8 x 1 + 3

We consider the new divisor 8 and the new remainder 3,and apply the division lemma to get

8 = 3 x 2 + 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 320 and 867 is 1

Notice that 1 = HCF(2,1) = HCF(3,2) = HCF(8,3) = HCF(11,8) = HCF(41,11) = HCF(93,41) = HCF(227,93) = HCF(320,227) = HCF(867,320) .

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

Step 1: Since 60 > 1, we apply the division lemma to 60 and 1, to get

60 = 1 x 60 + 0

The remainder has now become zero, so our procedure stops. Since the divisor at this stage is 1, the HCF of 1 and 60 is 1

Notice that 1 = HCF(60,1) .

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Frequently Asked Questions on HCF of 320, 867, 60 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 320, 867, 60?

Answer: HCF of 320, 867, 60 is 1 the largest number that divides all the numbers leaving a remainder zero.

3. How to find HCF of 320, 867, 60 using Euclid's Algorithm?

Answer: For arbitrary numbers 320, 867, 60 apply Euclid’s Division Lemma in succession until you obtain a remainder zero. HCF is the remainder in the last but one step.