Highest Common Factor of 406, 670, 661 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 406, 670, 661 i.e. 1 the largest integer that leaves a remainder zero for all numbers.

HCF of 406, 670, 661 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 406, 670, 661 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 406, 670, 661 is 1.

HCF(406, 670, 661) = 1

HCF of 406, 670, 661 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 406, 670, 661 is 1.

Highest Common Factor of 406,670,661 using Euclid's algorithm

Highest Common Factor of 406,670,661 is 1

Step 1: Since 670 > 406, we apply the division lemma to 670 and 406, to get

670 = 406 x 1 + 264

Step 2: Since the reminder 406 ≠ 0, we apply division lemma to 264 and 406, to get

406 = 264 x 1 + 142

Step 3: We consider the new divisor 264 and the new remainder 142, and apply the division lemma to get

264 = 142 x 1 + 122

We consider the new divisor 142 and the new remainder 122,and apply the division lemma to get

142 = 122 x 1 + 20

We consider the new divisor 122 and the new remainder 20,and apply the division lemma to get

122 = 20 x 6 + 2

We consider the new divisor 20 and the new remainder 2,and apply the division lemma to get

20 = 2 x 10 + 0

The remainder has now become zero, so our procedure stops. Since the divisor at this stage is 2, the HCF of 406 and 670 is 2

Notice that 2 = HCF(20,2) = HCF(122,20) = HCF(142,122) = HCF(264,142) = HCF(406,264) = HCF(670,406) .

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

Step 1: Since 661 > 2, we apply the division lemma to 661 and 2, to get

661 = 2 x 330 + 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 661 is 1

Notice that 1 = HCF(2,1) = HCF(661,2) .

HCF using Euclid's Algorithm Calculation Examples

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

Frequently Asked Questions on HCF of 406, 670, 661 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 406, 670, 661?

Answer: HCF of 406, 670, 661 is 1 the largest number that divides all the numbers leaving a remainder zero.

3. How to find HCF of 406, 670, 661 using Euclid's Algorithm?

Answer: For arbitrary numbers 406, 670, 661 apply Euclid’s Division Lemma in succession until you obtain a remainder zero. HCF is the remainder in the last but one step.