Highest Common Factor of 980, 410, 14 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 980, 410, 14 i.e. 2 the largest integer that leaves a remainder zero for all numbers.

HCF of 980, 410, 14 is 2 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 980, 410, 14 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 980, 410, 14 is 2.

HCF(980, 410, 14) = 2

HCF of 980, 410, 14 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 980, 410, 14 is 2.

Highest Common Factor of 980,410,14 using Euclid's algorithm

Highest Common Factor of 980,410,14 is 2

Step 1: Since 980 > 410, we apply the division lemma to 980 and 410, to get

980 = 410 x 2 + 160

Step 2: Since the reminder 410 ≠ 0, we apply division lemma to 160 and 410, to get

410 = 160 x 2 + 90

Step 3: We consider the new divisor 160 and the new remainder 90, and apply the division lemma to get

160 = 90 x 1 + 70

We consider the new divisor 90 and the new remainder 70,and apply the division lemma to get

90 = 70 x 1 + 20

We consider the new divisor 70 and the new remainder 20,and apply the division lemma to get

70 = 20 x 3 + 10

We consider the new divisor 20 and the new remainder 10,and apply the division lemma to get

20 = 10 x 2 + 0

The remainder has now become zero, so our procedure stops. Since the divisor at this stage is 10, the HCF of 980 and 410 is 10

Notice that 10 = HCF(20,10) = HCF(70,20) = HCF(90,70) = HCF(160,90) = HCF(410,160) = HCF(980,410) .


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

Step 1: Since 14 > 10, we apply the division lemma to 14 and 10, to get

14 = 10 x 1 + 4

Step 2: Since the reminder 10 ≠ 0, we apply division lemma to 4 and 10, to get

10 = 4 x 2 + 2

Step 3: We consider the new divisor 4 and the new remainder 2, and apply the division lemma to get

4 = 2 x 2 + 0

The remainder has now become zero, so our procedure stops. Since the divisor at this stage is 2, the HCF of 10 and 14 is 2

Notice that 2 = HCF(4,2) = HCF(10,4) = HCF(14,10) .

HCF using Euclid's Algorithm Calculation Examples

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

Frequently Asked Questions on HCF of 980, 410, 14 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 980, 410, 14?

Answer: HCF of 980, 410, 14 is 2 the largest number that divides all the numbers leaving a remainder zero.

3. How to find HCF of 980, 410, 14 using Euclid's Algorithm?

Answer: For arbitrary numbers 980, 410, 14 apply Euclid’s Division Lemma in succession until you obtain a remainder zero. HCF is the remainder in the last but one step.