Highest Common Factor of 221, 364, 450, 600 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 221, 364, 450, 600 i.e. 1 the largest integer that leaves a remainder zero for all numbers.

HCF of 221, 364, 450, 600 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 221, 364, 450, 600 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 221, 364, 450, 600 is 1.

HCF(221, 364, 450, 600) = 1

HCF of 221, 364, 450, 600 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 221, 364, 450, 600 is 1.

Highest Common Factor of 221,364,450,600 using Euclid's algorithm

Highest Common Factor of 221,364,450,600 is 1

Step 1: Since 364 > 221, we apply the division lemma to 364 and 221, to get

364 = 221 x 1 + 143

Step 2: Since the reminder 221 ≠ 0, we apply division lemma to 143 and 221, to get

221 = 143 x 1 + 78

Step 3: We consider the new divisor 143 and the new remainder 78, and apply the division lemma to get

143 = 78 x 1 + 65

We consider the new divisor 78 and the new remainder 65,and apply the division lemma to get

78 = 65 x 1 + 13

We consider the new divisor 65 and the new remainder 13,and apply the division lemma to get

65 = 13 x 5 + 0

The remainder has now become zero, so our procedure stops. Since the divisor at this stage is 13, the HCF of 221 and 364 is 13

Notice that 13 = HCF(65,13) = HCF(78,65) = HCF(143,78) = HCF(221,143) = HCF(364,221) .

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

Step 1: Since 450 > 13, we apply the division lemma to 450 and 13, to get

450 = 13 x 34 + 8

Step 2: Since the reminder 13 ≠ 0, we apply division lemma to 8 and 13, to get

13 = 8 x 1 + 5

Step 3: We consider the new divisor 8 and the new remainder 5, and apply the division lemma to get

8 = 5 x 1 + 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 13 and 450 is 1

Notice that 1 = HCF(2,1) = HCF(3,2) = HCF(5,3) = HCF(8,5) = HCF(13,8) = HCF(450,13) .

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

Step 1: Since 600 > 1, we apply the division lemma to 600 and 1, to get

600 = 1 x 600 + 0

The remainder has now become zero, so our procedure stops. Since the divisor at this stage is 1, the HCF of 1 and 600 is 1

Notice that 1 = HCF(600,1) .

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Frequently Asked Questions on HCF of 221, 364, 450, 600 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 221, 364, 450, 600?

Answer: HCF of 221, 364, 450, 600 is 1 the largest number that divides all the numbers leaving a remainder zero.

3. How to find HCF of 221, 364, 450, 600 using Euclid's Algorithm?

Answer: For arbitrary numbers 221, 364, 450, 600 apply Euclid’s Division Lemma in succession until you obtain a remainder zero. HCF is the remainder in the last but one step.