Highest Common Factor of 360, 821, 654 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 360, 821, 654 i.e. 1 the largest integer that leaves a remainder zero for all numbers.

HCF of 360, 821, 654 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 360, 821, 654 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 360, 821, 654 is 1.

HCF(360, 821, 654) = 1

HCF of 360, 821, 654 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 360, 821, 654 is 1.

Highest Common Factor of 360,821,654 using Euclid's algorithm

Highest Common Factor of 360,821,654 is 1

Step 1: Since 821 > 360, we apply the division lemma to 821 and 360, to get

821 = 360 x 2 + 101

Step 2: Since the reminder 360 ≠ 0, we apply division lemma to 101 and 360, to get

360 = 101 x 3 + 57

Step 3: We consider the new divisor 101 and the new remainder 57, and apply the division lemma to get

101 = 57 x 1 + 44

We consider the new divisor 57 and the new remainder 44,and apply the division lemma to get

57 = 44 x 1 + 13

We consider the new divisor 44 and the new remainder 13,and apply the division lemma to get

44 = 13 x 3 + 5

We consider the new divisor 13 and the new remainder 5,and apply the division lemma to get

13 = 5 x 2 + 3

We consider the new divisor 5 and the new remainder 3,and apply the division lemma to get

5 = 3 x 1 + 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 360 and 821 is 1

Notice that 1 = HCF(2,1) = HCF(3,2) = HCF(5,3) = HCF(13,5) = HCF(44,13) = HCF(57,44) = HCF(101,57) = HCF(360,101) = HCF(821,360) .

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

Step 1: Since 654 > 1, we apply the division lemma to 654 and 1, to get

654 = 1 x 654 + 0

The remainder has now become zero, so our procedure stops. Since the divisor at this stage is 1, the HCF of 1 and 654 is 1

Notice that 1 = HCF(654,1) .

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Frequently Asked Questions on HCF of 360, 821, 654 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 360, 821, 654?

Answer: HCF of 360, 821, 654 is 1 the largest number that divides all the numbers leaving a remainder zero.

3. How to find HCF of 360, 821, 654 using Euclid's Algorithm?

Answer: For arbitrary numbers 360, 821, 654 apply Euclid’s Division Lemma in succession until you obtain a remainder zero. HCF is the remainder in the last but one step.