Highest Common Factor of 522, 200, 216 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 522, 200, 216 i.e. 2 the largest integer that leaves a remainder zero for all numbers.

HCF of 522, 200, 216 is 2 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 522, 200, 216 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 522, 200, 216 is 2.

HCF(522, 200, 216) = 2

HCF of 522, 200, 216 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 522, 200, 216 is 2.

Highest Common Factor of 522,200,216 using Euclid's algorithm

Highest Common Factor of 522,200,216 is 2

Step 1: Since 522 > 200, we apply the division lemma to 522 and 200, to get

522 = 200 x 2 + 122

Step 2: Since the reminder 200 ≠ 0, we apply division lemma to 122 and 200, to get

200 = 122 x 1 + 78

Step 3: We consider the new divisor 122 and the new remainder 78, and apply the division lemma to get

122 = 78 x 1 + 44

We consider the new divisor 78 and the new remainder 44,and apply the division lemma to get

78 = 44 x 1 + 34

We consider the new divisor 44 and the new remainder 34,and apply the division lemma to get

44 = 34 x 1 + 10

We consider the new divisor 34 and the new remainder 10,and apply the division lemma to get

34 = 10 x 3 + 4

We consider the new divisor 10 and the new remainder 4,and apply the division lemma to get

10 = 4 x 2 + 2

We consider the new divisor 4 and the new remainder 2,and apply the division lemma to get

4 = 2 x 2 + 0

The remainder has now become zero, so our procedure stops. Since the divisor at this stage is 2, the HCF of 522 and 200 is 2

Notice that 2 = HCF(4,2) = HCF(10,4) = HCF(34,10) = HCF(44,34) = HCF(78,44) = HCF(122,78) = HCF(200,122) = HCF(522,200) .

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

Step 1: Since 216 > 2, we apply the division lemma to 216 and 2, to get

216 = 2 x 108 + 0

The remainder has now become zero, so our procedure stops. Since the divisor at this stage is 2, the HCF of 2 and 216 is 2

Notice that 2 = HCF(216,2) .

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Frequently Asked Questions on HCF of 522, 200, 216 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 522, 200, 216?

Answer: HCF of 522, 200, 216 is 2 the largest number that divides all the numbers leaving a remainder zero.

3. How to find HCF of 522, 200, 216 using Euclid's Algorithm?

Answer: For arbitrary numbers 522, 200, 216 apply Euclid’s Division Lemma in succession until you obtain a remainder zero. HCF is the remainder in the last but one step.