Highest Common Factor of 600, 926, 666 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 600, 926, 666 i.e. 2 the largest integer that leaves a remainder zero for all numbers.

HCF of 600, 926, 666 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 600, 926, 666 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 600, 926, 666 is 2.

HCF(600, 926, 666) = 2

HCF of 600, 926, 666 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 600, 926, 666 is 2.

Highest Common Factor of 600,926,666 using Euclid's algorithm

Highest Common Factor of 600,926,666 is 2

Step 1: Since 926 > 600, we apply the division lemma to 926 and 600, to get

926 = 600 x 1 + 326

Step 2: Since the reminder 600 ≠ 0, we apply division lemma to 326 and 600, to get

600 = 326 x 1 + 274

Step 3: We consider the new divisor 326 and the new remainder 274, and apply the division lemma to get

326 = 274 x 1 + 52

We consider the new divisor 274 and the new remainder 52,and apply the division lemma to get

274 = 52 x 5 + 14

We consider the new divisor 52 and the new remainder 14,and apply the division lemma to get

52 = 14 x 3 + 10

We consider the new divisor 14 and the new remainder 10,and apply the division lemma to get

14 = 10 x 1 + 4

We consider the new divisor 10 and the new remainder 4,and apply the division lemma to get

10 = 4 x 2 + 2

We consider the new divisor 4 and the new remainder 2,and apply the division lemma to get

4 = 2 x 2 + 0

The remainder has now become zero, so our procedure stops. Since the divisor at this stage is 2, the HCF of 600 and 926 is 2

Notice that 2 = HCF(4,2) = HCF(10,4) = HCF(14,10) = HCF(52,14) = HCF(274,52) = HCF(326,274) = HCF(600,326) = HCF(926,600) .

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

Step 1: Since 666 > 2, we apply the division lemma to 666 and 2, to get

666 = 2 x 333 + 0

The remainder has now become zero, so our procedure stops. Since the divisor at this stage is 2, the HCF of 2 and 666 is 2

Notice that 2 = HCF(666,2) .

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Frequently Asked Questions on HCF of 600, 926, 666 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 600, 926, 666?

Answer: HCF of 600, 926, 666 is 2 the largest number that divides all the numbers leaving a remainder zero.

3. How to find HCF of 600, 926, 666 using Euclid's Algorithm?

Answer: For arbitrary numbers 600, 926, 666 apply Euclid’s Division Lemma in succession until you obtain a remainder zero. HCF is the remainder in the last but one step.