Highest Common Factor of 9986, 7157, 37469 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 9986, 7157, 37469 i.e. 1 the largest integer that leaves a remainder zero for all numbers.

HCF of 9986, 7157, 37469 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 9986, 7157, 37469 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 9986, 7157, 37469 is 1.

HCF(9986, 7157, 37469) = 1

HCF of 9986, 7157, 37469 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 9986, 7157, 37469 is 1.

Highest Common Factor of 9986,7157,37469 using Euclid's algorithm

Highest Common Factor of 9986,7157,37469 is 1

Step 1: Since 9986 > 7157, we apply the division lemma to 9986 and 7157, to get

9986 = 7157 x 1 + 2829

Step 2: Since the reminder 7157 ≠ 0, we apply division lemma to 2829 and 7157, to get

7157 = 2829 x 2 + 1499

Step 3: We consider the new divisor 2829 and the new remainder 1499, and apply the division lemma to get

2829 = 1499 x 1 + 1330

We consider the new divisor 1499 and the new remainder 1330,and apply the division lemma to get

1499 = 1330 x 1 + 169

We consider the new divisor 1330 and the new remainder 169,and apply the division lemma to get

1330 = 169 x 7 + 147

We consider the new divisor 169 and the new remainder 147,and apply the division lemma to get

169 = 147 x 1 + 22

We consider the new divisor 147 and the new remainder 22,and apply the division lemma to get

147 = 22 x 6 + 15

We consider the new divisor 22 and the new remainder 15,and apply the division lemma to get

22 = 15 x 1 + 7

We consider the new divisor 15 and the new remainder 7,and apply the division lemma to get

15 = 7 x 2 + 1

We consider the new divisor 7 and the new remainder 1,and apply the division lemma to get

7 = 1 x 7 + 0

The remainder has now become zero, so our procedure stops. Since the divisor at this stage is 1, the HCF of 9986 and 7157 is 1

Notice that 1 = HCF(7,1) = HCF(15,7) = HCF(22,15) = HCF(147,22) = HCF(169,147) = HCF(1330,169) = HCF(1499,1330) = HCF(2829,1499) = HCF(7157,2829) = HCF(9986,7157) .

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

Step 1: Since 37469 > 1, we apply the division lemma to 37469 and 1, to get

37469 = 1 x 37469 + 0

The remainder has now become zero, so our procedure stops. Since the divisor at this stage is 1, the HCF of 1 and 37469 is 1

Notice that 1 = HCF(37469,1) .

HCF using Euclid's Algorithm Calculation Examples

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

Frequently Asked Questions on HCF of 9986, 7157, 37469 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 9986, 7157, 37469?

Answer: HCF of 9986, 7157, 37469 is 1 the largest number that divides all the numbers leaving a remainder zero.

3. How to find HCF of 9986, 7157, 37469 using Euclid's Algorithm?

Answer: For arbitrary numbers 9986, 7157, 37469 apply Euclid’s Division Lemma in succession until you obtain a remainder zero. HCF is the remainder in the last but one step.