Highest Common Factor of 521, 848, 522 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 521, 848, 522 i.e. 1 the largest integer that leaves a remainder zero for all numbers.

HCF of 521, 848, 522 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 521, 848, 522 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 521, 848, 522 is 1.

HCF(521, 848, 522) = 1

HCF of 521, 848, 522 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 521, 848, 522 is 1.

Highest Common Factor of 521,848,522 using Euclid's algorithm

Highest Common Factor of 521,848,522 is 1

Step 1: Since 848 > 521, we apply the division lemma to 848 and 521, to get

848 = 521 x 1 + 327

Step 2: Since the reminder 521 ≠ 0, we apply division lemma to 327 and 521, to get

521 = 327 x 1 + 194

Step 3: We consider the new divisor 327 and the new remainder 194, and apply the division lemma to get

327 = 194 x 1 + 133

We consider the new divisor 194 and the new remainder 133,and apply the division lemma to get

194 = 133 x 1 + 61

We consider the new divisor 133 and the new remainder 61,and apply the division lemma to get

133 = 61 x 2 + 11

We consider the new divisor 61 and the new remainder 11,and apply the division lemma to get

61 = 11 x 5 + 6

We consider the new divisor 11 and the new remainder 6,and apply the division lemma to get

11 = 6 x 1 + 5

We consider the new divisor 6 and the new remainder 5,and apply the division lemma to get

6 = 5 x 1 + 1

We consider the new divisor 5 and the new remainder 1,and apply the division lemma to get

5 = 1 x 5 + 0

The remainder has now become zero, so our procedure stops. Since the divisor at this stage is 1, the HCF of 521 and 848 is 1

Notice that 1 = HCF(5,1) = HCF(6,5) = HCF(11,6) = HCF(61,11) = HCF(133,61) = HCF(194,133) = HCF(327,194) = HCF(521,327) = HCF(848,521) .

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

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

522 = 1 x 522 + 0

The remainder has now become zero, so our procedure stops. Since the divisor at this stage is 1, the HCF of 1 and 522 is 1

Notice that 1 = HCF(522,1) .

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Frequently Asked Questions on HCF of 521, 848, 522 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 521, 848, 522?

Answer: HCF of 521, 848, 522 is 1 the largest number that divides all the numbers leaving a remainder zero.

3. How to find HCF of 521, 848, 522 using Euclid's Algorithm?

Answer: For arbitrary numbers 521, 848, 522 apply Euclid’s Division Lemma in succession until you obtain a remainder zero. HCF is the remainder in the last but one step.