Highest Common Factor of 528, 814, 668 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 528, 814, 668 i.e. 2 the largest integer that leaves a remainder zero for all numbers.

HCF of 528, 814, 668 is 2 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 528, 814, 668 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 528, 814, 668 is 2.

HCF(528, 814, 668) = 2

HCF of 528, 814, 668 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 528, 814, 668 is 2.

Highest Common Factor of 528,814,668 using Euclid's algorithm

Highest Common Factor of 528,814,668 is 2

Step 1: Since 814 > 528, we apply the division lemma to 814 and 528, to get

814 = 528 x 1 + 286

Step 2: Since the reminder 528 ≠ 0, we apply division lemma to 286 and 528, to get

528 = 286 x 1 + 242

Step 3: We consider the new divisor 286 and the new remainder 242, and apply the division lemma to get

286 = 242 x 1 + 44

We consider the new divisor 242 and the new remainder 44,and apply the division lemma to get

242 = 44 x 5 + 22

We consider the new divisor 44 and the new remainder 22,and apply the division lemma to get

44 = 22 x 2 + 0

The remainder has now become zero, so our procedure stops. Since the divisor at this stage is 22, the HCF of 528 and 814 is 22

Notice that 22 = HCF(44,22) = HCF(242,44) = HCF(286,242) = HCF(528,286) = HCF(814,528) .

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

Step 1: Since 668 > 22, we apply the division lemma to 668 and 22, to get

668 = 22 x 30 + 8

Step 2: Since the reminder 22 ≠ 0, we apply division lemma to 8 and 22, to get

22 = 8 x 2 + 6

Step 3: We consider the new divisor 8 and the new remainder 6, and apply the division lemma to get

8 = 6 x 1 + 2

We consider the new divisor 6 and the new remainder 2, and apply the division lemma to get

6 = 2 x 3 + 0

The remainder has now become zero, so our procedure stops. Since the divisor at this stage is 2, the HCF of 22 and 668 is 2

Notice that 2 = HCF(6,2) = HCF(8,6) = HCF(22,8) = HCF(668,22) .

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Frequently Asked Questions on HCF of 528, 814, 668 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 528, 814, 668?

Answer: HCF of 528, 814, 668 is 2 the largest number that divides all the numbers leaving a remainder zero.

3. How to find HCF of 528, 814, 668 using Euclid's Algorithm?

Answer: For arbitrary numbers 528, 814, 668 apply Euclid’s Division Lemma in succession until you obtain a remainder zero. HCF is the remainder in the last but one step.