Highest Common Factor of 858, 473, 524 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 858, 473, 524 i.e. 1 the largest integer that leaves a remainder zero for all numbers.

HCF of 858, 473, 524 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 858, 473, 524 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 858, 473, 524 is 1.

HCF(858, 473, 524) = 1

HCF of 858, 473, 524 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 858, 473, 524 is 1.

Highest Common Factor of 858,473,524 using Euclid's algorithm

Highest Common Factor of 858,473,524 is 1

Step 1: Since 858 > 473, we apply the division lemma to 858 and 473, to get

858 = 473 x 1 + 385

Step 2: Since the reminder 473 ≠ 0, we apply division lemma to 385 and 473, to get

473 = 385 x 1 + 88

Step 3: We consider the new divisor 385 and the new remainder 88, and apply the division lemma to get

385 = 88 x 4 + 33

We consider the new divisor 88 and the new remainder 33,and apply the division lemma to get

88 = 33 x 2 + 22

We consider the new divisor 33 and the new remainder 22,and apply the division lemma to get

33 = 22 x 1 + 11

We consider the new divisor 22 and the new remainder 11,and apply the division lemma to get

22 = 11 x 2 + 0

The remainder has now become zero, so our procedure stops. Since the divisor at this stage is 11, the HCF of 858 and 473 is 11

Notice that 11 = HCF(22,11) = HCF(33,22) = HCF(88,33) = HCF(385,88) = HCF(473,385) = HCF(858,473) .

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

Step 1: Since 524 > 11, we apply the division lemma to 524 and 11, to get

524 = 11 x 47 + 7

Step 2: Since the reminder 11 ≠ 0, we apply division lemma to 7 and 11, to get

11 = 7 x 1 + 4

Step 3: We consider the new divisor 7 and the new remainder 4, and apply the division lemma to get

7 = 4 x 1 + 3

We consider the new divisor 4 and the new remainder 3,and apply the division lemma to get

4 = 3 x 1 + 1

We consider the new divisor 3 and the new remainder 1,and apply the division lemma to get

3 = 1 x 3 + 0

The remainder has now become zero, so our procedure stops. Since the divisor at this stage is 1, the HCF of 11 and 524 is 1

Notice that 1 = HCF(3,1) = HCF(4,3) = HCF(7,4) = HCF(11,7) = HCF(524,11) .

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Frequently Asked Questions on HCF of 858, 473, 524 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 858, 473, 524?

Answer: HCF of 858, 473, 524 is 1 the largest number that divides all the numbers leaving a remainder zero.

3. How to find HCF of 858, 473, 524 using Euclid's Algorithm?

Answer: For arbitrary numbers 858, 473, 524 apply Euclid’s Division Lemma in succession until you obtain a remainder zero. HCF is the remainder in the last but one step.