Highest Common Factor of 407, 1379, 8688 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 407, 1379, 8688 i.e. 1 the largest integer that leaves a remainder zero for all numbers.

HCF of 407, 1379, 8688 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 407, 1379, 8688 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 407, 1379, 8688 is 1.

HCF(407, 1379, 8688) = 1

HCF of 407, 1379, 8688 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 407, 1379, 8688 is 1.

Highest Common Factor of 407,1379,8688 using Euclid's algorithm

Highest Common Factor of 407,1379,8688 is 1

Step 1: Since 1379 > 407, we apply the division lemma to 1379 and 407, to get

1379 = 407 x 3 + 158

Step 2: Since the reminder 407 ≠ 0, we apply division lemma to 158 and 407, to get

407 = 158 x 2 + 91

Step 3: We consider the new divisor 158 and the new remainder 91, and apply the division lemma to get

158 = 91 x 1 + 67

We consider the new divisor 91 and the new remainder 67,and apply the division lemma to get

91 = 67 x 1 + 24

We consider the new divisor 67 and the new remainder 24,and apply the division lemma to get

67 = 24 x 2 + 19

We consider the new divisor 24 and the new remainder 19,and apply the division lemma to get

24 = 19 x 1 + 5

We consider the new divisor 19 and the new remainder 5,and apply the division lemma to get

19 = 5 x 3 + 4

We consider the new divisor 5 and the new remainder 4,and apply the division lemma to get

5 = 4 x 1 + 1

We consider the new divisor 4 and the new remainder 1,and apply the division lemma to get

4 = 1 x 4 + 0

The remainder has now become zero, so our procedure stops. Since the divisor at this stage is 1, the HCF of 407 and 1379 is 1

Notice that 1 = HCF(4,1) = HCF(5,4) = HCF(19,5) = HCF(24,19) = HCF(67,24) = HCF(91,67) = HCF(158,91) = HCF(407,158) = HCF(1379,407) .

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

Step 1: Since 8688 > 1, we apply the division lemma to 8688 and 1, to get

8688 = 1 x 8688 + 0

The remainder has now become zero, so our procedure stops. Since the divisor at this stage is 1, the HCF of 1 and 8688 is 1

Notice that 1 = HCF(8688,1) .

HCF using Euclid's Algorithm Calculation Examples

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

Frequently Asked Questions on HCF of 407, 1379, 8688 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 407, 1379, 8688?

Answer: HCF of 407, 1379, 8688 is 1 the largest number that divides all the numbers leaving a remainder zero.

3. How to find HCF of 407, 1379, 8688 using Euclid's Algorithm?

Answer: For arbitrary numbers 407, 1379, 8688 apply Euclid’s Division Lemma in succession until you obtain a remainder zero. HCF is the remainder in the last but one step.