Highest Common Factor of 523, 826, 852 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 523, 826, 852 i.e. 1 the largest integer that leaves a remainder zero for all numbers.

HCF of 523, 826, 852 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 523, 826, 852 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 523, 826, 852 is 1.

HCF(523, 826, 852) = 1

HCF of 523, 826, 852 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 523, 826, 852 is 1.

Highest Common Factor of 523,826,852 using Euclid's algorithm

Highest Common Factor of 523,826,852 is 1

Step 1: Since 826 > 523, we apply the division lemma to 826 and 523, to get

826 = 523 x 1 + 303

Step 2: Since the reminder 523 ≠ 0, we apply division lemma to 303 and 523, to get

523 = 303 x 1 + 220

Step 3: We consider the new divisor 303 and the new remainder 220, and apply the division lemma to get

303 = 220 x 1 + 83

We consider the new divisor 220 and the new remainder 83,and apply the division lemma to get

220 = 83 x 2 + 54

We consider the new divisor 83 and the new remainder 54,and apply the division lemma to get

83 = 54 x 1 + 29

We consider the new divisor 54 and the new remainder 29,and apply the division lemma to get

54 = 29 x 1 + 25

We consider the new divisor 29 and the new remainder 25,and apply the division lemma to get

29 = 25 x 1 + 4

We consider the new divisor 25 and the new remainder 4,and apply the division lemma to get

25 = 4 x 6 + 1

We consider the new divisor 4 and the new remainder 1,and apply the division lemma to get

4 = 1 x 4 + 0

The remainder has now become zero, so our procedure stops. Since the divisor at this stage is 1, the HCF of 523 and 826 is 1

Notice that 1 = HCF(4,1) = HCF(25,4) = HCF(29,25) = HCF(54,29) = HCF(83,54) = HCF(220,83) = HCF(303,220) = HCF(523,303) = HCF(826,523) .

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

Step 1: Since 852 > 1, we apply the division lemma to 852 and 1, to get

852 = 1 x 852 + 0

The remainder has now become zero, so our procedure stops. Since the divisor at this stage is 1, the HCF of 1 and 852 is 1

Notice that 1 = HCF(852,1) .

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Frequently Asked Questions on HCF of 523, 826, 852 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 523, 826, 852?

Answer: HCF of 523, 826, 852 is 1 the largest number that divides all the numbers leaving a remainder zero.

3. How to find HCF of 523, 826, 852 using Euclid's Algorithm?

Answer: For arbitrary numbers 523, 826, 852 apply Euclid’s Division Lemma in succession until you obtain a remainder zero. HCF is the remainder in the last but one step.