Highest Common Factor of 660, 933, 923 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 660, 933, 923 i.e. 1 the largest integer that leaves a remainder zero for all numbers.

HCF of 660, 933, 923 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 660, 933, 923 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 660, 933, 923 is 1.

HCF(660, 933, 923) = 1

HCF of 660, 933, 923 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 660, 933, 923 is 1.

Highest Common Factor of 660,933,923 using Euclid's algorithm

Highest Common Factor of 660,933,923 is 1

Step 1: Since 933 > 660, we apply the division lemma to 933 and 660, to get

933 = 660 x 1 + 273

Step 2: Since the reminder 660 ≠ 0, we apply division lemma to 273 and 660, to get

660 = 273 x 2 + 114

Step 3: We consider the new divisor 273 and the new remainder 114, and apply the division lemma to get

273 = 114 x 2 + 45

We consider the new divisor 114 and the new remainder 45,and apply the division lemma to get

114 = 45 x 2 + 24

We consider the new divisor 45 and the new remainder 24,and apply the division lemma to get

45 = 24 x 1 + 21

We consider the new divisor 24 and the new remainder 21,and apply the division lemma to get

24 = 21 x 1 + 3

We consider the new divisor 21 and the new remainder 3,and apply the division lemma to get

21 = 3 x 7 + 0

The remainder has now become zero, so our procedure stops. Since the divisor at this stage is 3, the HCF of 660 and 933 is 3

Notice that 3 = HCF(21,3) = HCF(24,21) = HCF(45,24) = HCF(114,45) = HCF(273,114) = HCF(660,273) = HCF(933,660) .

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

Step 1: Since 923 > 3, we apply the division lemma to 923 and 3, to get

923 = 3 x 307 + 2

Step 2: Since the reminder 3 ≠ 0, we apply division lemma to 2 and 3, to get

3 = 2 x 1 + 1

Step 3: We consider the new divisor 2 and the new remainder 1, and apply the division lemma to get

2 = 1 x 2 + 0

The remainder has now become zero, so our procedure stops. Since the divisor at this stage is 1, the HCF of 3 and 923 is 1

Notice that 1 = HCF(2,1) = HCF(3,2) = HCF(923,3) .

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Frequently Asked Questions on HCF of 660, 933, 923 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 660, 933, 923?

Answer: HCF of 660, 933, 923 is 1 the largest number that divides all the numbers leaving a remainder zero.

3. How to find HCF of 660, 933, 923 using Euclid's Algorithm?

Answer: For arbitrary numbers 660, 933, 923 apply Euclid’s Division Lemma in succession until you obtain a remainder zero. HCF is the remainder in the last but one step.