Highest Common Factor of 523, 878, 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 523, 878, 668 i.e. 1 the largest integer that leaves a remainder zero for all numbers.

HCF of 523, 878, 668 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, 878, 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 523, 878, 668 is 1.

HCF(523, 878, 668) = 1

HCF of 523, 878, 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 523, 878, 668 is 1.

Highest Common Factor of 523,878,668 using Euclid's algorithm

Highest Common Factor of 523,878,668 is 1

Step 1: Since 878 > 523, we apply the division lemma to 878 and 523, to get

878 = 523 x 1 + 355

Step 2: Since the reminder 523 ≠ 0, we apply division lemma to 355 and 523, to get

523 = 355 x 1 + 168

Step 3: We consider the new divisor 355 and the new remainder 168, and apply the division lemma to get

355 = 168 x 2 + 19

We consider the new divisor 168 and the new remainder 19,and apply the division lemma to get

168 = 19 x 8 + 16

We consider the new divisor 19 and the new remainder 16,and apply the division lemma to get

19 = 16 x 1 + 3

We consider the new divisor 16 and the new remainder 3,and apply the division lemma to get

16 = 3 x 5 + 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 523 and 878 is 1

Notice that 1 = HCF(3,1) = HCF(16,3) = HCF(19,16) = HCF(168,19) = HCF(355,168) = HCF(523,355) = HCF(878,523) .

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

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

668 = 1 x 668 + 0

The remainder has now become zero, so our procedure stops. Since the divisor at this stage is 1, the HCF of 1 and 668 is 1

Notice that 1 = HCF(668,1) .

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Frequently Asked Questions on HCF of 523, 878, 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 523, 878, 668?

Answer: HCF of 523, 878, 668 is 1 the largest number that divides all the numbers leaving a remainder zero.

3. How to find HCF of 523, 878, 668 using Euclid's Algorithm?

Answer: For arbitrary numbers 523, 878, 668 apply Euclid’s Division Lemma in succession until you obtain a remainder zero. HCF is the remainder in the last but one step.