Highest Common Factor of 899, 709, 731 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 899, 709, 731 i.e. 1 the largest integer that leaves a remainder zero for all numbers.

HCF of 899, 709, 731 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 899, 709, 731 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 899, 709, 731 is 1.

HCF(899, 709, 731) = 1

HCF of 899, 709, 731 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 899, 709, 731 is 1.

Highest Common Factor of 899,709,731 using Euclid's algorithm

Highest Common Factor of 899,709,731 is 1

Step 1: Since 899 > 709, we apply the division lemma to 899 and 709, to get

899 = 709 x 1 + 190

Step 2: Since the reminder 709 ≠ 0, we apply division lemma to 190 and 709, to get

709 = 190 x 3 + 139

Step 3: We consider the new divisor 190 and the new remainder 139, and apply the division lemma to get

190 = 139 x 1 + 51

We consider the new divisor 139 and the new remainder 51,and apply the division lemma to get

139 = 51 x 2 + 37

We consider the new divisor 51 and the new remainder 37,and apply the division lemma to get

51 = 37 x 1 + 14

We consider the new divisor 37 and the new remainder 14,and apply the division lemma to get

37 = 14 x 2 + 9

We consider the new divisor 14 and the new remainder 9,and apply the division lemma to get

14 = 9 x 1 + 5

We consider the new divisor 9 and the new remainder 5,and apply the division lemma to get

9 = 5 x 1 + 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 899 and 709 is 1

Notice that 1 = HCF(4,1) = HCF(5,4) = HCF(9,5) = HCF(14,9) = HCF(37,14) = HCF(51,37) = HCF(139,51) = HCF(190,139) = HCF(709,190) = HCF(899,709) .

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

Step 1: Since 731 > 1, we apply the division lemma to 731 and 1, to get

731 = 1 x 731 + 0

The remainder has now become zero, so our procedure stops. Since the divisor at this stage is 1, the HCF of 1 and 731 is 1

Notice that 1 = HCF(731,1) .

HCF using Euclid's Algorithm Calculation Examples

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

Frequently Asked Questions on HCF of 899, 709, 731 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 899, 709, 731?

Answer: HCF of 899, 709, 731 is 1 the largest number that divides all the numbers leaving a remainder zero.

3. How to find HCF of 899, 709, 731 using Euclid's Algorithm?

Answer: For arbitrary numbers 899, 709, 731 apply Euclid’s Division Lemma in succession until you obtain a remainder zero. HCF is the remainder in the last but one step.