Highest Common Factor of 522, 348, 993 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, 348, 993 i.e. 3 the largest integer that leaves a remainder zero for all numbers.

HCF of 522, 348, 993 is 3 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, 348, 993 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, 348, 993 is 3.

HCF(522, 348, 993) = 3

HCF of 522, 348, 993 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, 348, 993 is 3.

Highest Common Factor of 522,348,993 using Euclid's algorithm

Highest Common Factor of 522,348,993 is 3

Step 1: Since 522 > 348, we apply the division lemma to 522 and 348, to get

522 = 348 x 1 + 174

Step 2: Since the reminder 348 ≠ 0, we apply division lemma to 174 and 348, to get

348 = 174 x 2 + 0

The remainder has now become zero, so our procedure stops. Since the divisor at this stage is 174, the HCF of 522 and 348 is 174

Notice that 174 = HCF(348,174) = HCF(522,348) .


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

Step 1: Since 993 > 174, we apply the division lemma to 993 and 174, to get

993 = 174 x 5 + 123

Step 2: Since the reminder 174 ≠ 0, we apply division lemma to 123 and 174, to get

174 = 123 x 1 + 51

Step 3: We consider the new divisor 123 and the new remainder 51, and apply the division lemma to get

123 = 51 x 2 + 21

We consider the new divisor 51 and the new remainder 21,and apply the division lemma to get

51 = 21 x 2 + 9

We consider the new divisor 21 and the new remainder 9,and apply the division lemma to get

21 = 9 x 2 + 3

We consider the new divisor 9 and the new remainder 3,and apply the division lemma to get

9 = 3 x 3 + 0

The remainder has now become zero, so our procedure stops. Since the divisor at this stage is 3, the HCF of 174 and 993 is 3

Notice that 3 = HCF(9,3) = HCF(21,9) = HCF(51,21) = HCF(123,51) = HCF(174,123) = HCF(993,174) .

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Frequently Asked Questions on HCF of 522, 348, 993 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, 348, 993?

Answer: HCF of 522, 348, 993 is 3 the largest number that divides all the numbers leaving a remainder zero.

3. How to find HCF of 522, 348, 993 using Euclid's Algorithm?

Answer: For arbitrary numbers 522, 348, 993 apply Euclid’s Division Lemma in succession until you obtain a remainder zero. HCF is the remainder in the last but one step.