Highest Common Factor of 522, 632, 133 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, 632, 133 i.e. 1 the largest integer that leaves a remainder zero for all numbers.

HCF of 522, 632, 133 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 522, 632, 133 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, 632, 133 is 1.

HCF(522, 632, 133) = 1

HCF of 522, 632, 133 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, 632, 133 is 1.

Highest Common Factor of 522,632,133 using Euclid's algorithm

Highest Common Factor of 522,632,133 is 1

Step 1: Since 632 > 522, we apply the division lemma to 632 and 522, to get

632 = 522 x 1 + 110

Step 2: Since the reminder 522 ≠ 0, we apply division lemma to 110 and 522, to get

522 = 110 x 4 + 82

Step 3: We consider the new divisor 110 and the new remainder 82, and apply the division lemma to get

110 = 82 x 1 + 28

We consider the new divisor 82 and the new remainder 28,and apply the division lemma to get

82 = 28 x 2 + 26

We consider the new divisor 28 and the new remainder 26,and apply the division lemma to get

28 = 26 x 1 + 2

We consider the new divisor 26 and the new remainder 2,and apply the division lemma to get

26 = 2 x 13 + 0

The remainder has now become zero, so our procedure stops. Since the divisor at this stage is 2, the HCF of 522 and 632 is 2

Notice that 2 = HCF(26,2) = HCF(28,26) = HCF(82,28) = HCF(110,82) = HCF(522,110) = HCF(632,522) .

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

Step 1: Since 133 > 2, we apply the division lemma to 133 and 2, to get

133 = 2 x 66 + 1

Step 2: Since the reminder 2 ≠ 0, we apply division lemma to 1 and 2, 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 2 and 133 is 1

Notice that 1 = HCF(2,1) = HCF(133,2) .

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Frequently Asked Questions on HCF of 522, 632, 133 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, 632, 133?

Answer: HCF of 522, 632, 133 is 1 the largest number that divides all the numbers leaving a remainder zero.

3. How to find HCF of 522, 632, 133 using Euclid's Algorithm?

Answer: For arbitrary numbers 522, 632, 133 apply Euclid’s Division Lemma in succession until you obtain a remainder zero. HCF is the remainder in the last but one step.