Highest Common Factor of 66, 40, 667 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 66, 40, 667 i.e. 1 the largest integer that leaves a remainder zero for all numbers.

HCF of 66, 40, 667 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 66, 40, 667 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 66, 40, 667 is 1.

HCF(66, 40, 667) = 1

HCF of 66, 40, 667 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 66, 40, 667 is 1.

Highest Common Factor of 66,40,667 using Euclid's algorithm

Highest Common Factor of 66,40,667 is 1

Step 1: Since 66 > 40, we apply the division lemma to 66 and 40, to get

66 = 40 x 1 + 26

Step 2: Since the reminder 40 ≠ 0, we apply division lemma to 26 and 40, to get

40 = 26 x 1 + 14

Step 3: We consider the new divisor 26 and the new remainder 14, and apply the division lemma to get

26 = 14 x 1 + 12

We consider the new divisor 14 and the new remainder 12,and apply the division lemma to get

14 = 12 x 1 + 2

We consider the new divisor 12 and the new remainder 2,and apply the division lemma to get

12 = 2 x 6 + 0

The remainder has now become zero, so our procedure stops. Since the divisor at this stage is 2, the HCF of 66 and 40 is 2

Notice that 2 = HCF(12,2) = HCF(14,12) = HCF(26,14) = HCF(40,26) = HCF(66,40) .

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

Step 1: Since 667 > 2, we apply the division lemma to 667 and 2, to get

667 = 2 x 333 + 1

Step 2: Since the reminder 2 ≠ 0, we apply division lemma to 1 and 2, 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 2 and 667 is 1

Notice that 1 = HCF(2,1) = HCF(667,2) .

HCF using Euclid's Algorithm Calculation Examples

Here are some samples of HCF using Euclid's Algorithm calculations.

Frequently Asked Questions on HCF of 66, 40, 667 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 66, 40, 667?

Answer: HCF of 66, 40, 667 is 1 the largest number that divides all the numbers leaving a remainder zero.

3. How to find HCF of 66, 40, 667 using Euclid's Algorithm?

Answer: For arbitrary numbers 66, 40, 667 apply Euclid’s Division Lemma in succession until you obtain a remainder zero. HCF is the remainder in the last but one step.