Highest Common Factor of 990, 559, 970 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 990, 559, 970 i.e. 1 the largest integer that leaves a remainder zero for all numbers.

HCF of 990, 559, 970 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 990, 559, 970 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 990, 559, 970 is 1.

HCF(990, 559, 970) = 1

HCF of 990, 559, 970 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 990, 559, 970 is 1.

Highest Common Factor of 990,559,970 using Euclid's algorithm

Highest Common Factor of 990,559,970 is 1

Step 1: Since 990 > 559, we apply the division lemma to 990 and 559, to get

990 = 559 x 1 + 431

Step 2: Since the reminder 559 ≠ 0, we apply division lemma to 431 and 559, to get

559 = 431 x 1 + 128

Step 3: We consider the new divisor 431 and the new remainder 128, and apply the division lemma to get

431 = 128 x 3 + 47

We consider the new divisor 128 and the new remainder 47,and apply the division lemma to get

128 = 47 x 2 + 34

We consider the new divisor 47 and the new remainder 34,and apply the division lemma to get

47 = 34 x 1 + 13

We consider the new divisor 34 and the new remainder 13,and apply the division lemma to get

34 = 13 x 2 + 8

We consider the new divisor 13 and the new remainder 8,and apply the division lemma to get

13 = 8 x 1 + 5

We consider the new divisor 8 and the new remainder 5,and apply the division lemma to get

8 = 5 x 1 + 3

We consider the new divisor 5 and the new remainder 3,and apply the division lemma to get

5 = 3 x 1 + 2

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

3 = 2 x 1 + 1

We consider the new divisor 2 and the new remainder 1,and apply the division lemma 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 990 and 559 is 1

Notice that 1 = HCF(2,1) = HCF(3,2) = HCF(5,3) = HCF(8,5) = HCF(13,8) = HCF(34,13) = HCF(47,34) = HCF(128,47) = HCF(431,128) = HCF(559,431) = HCF(990,559) .

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

Step 1: Since 970 > 1, we apply the division lemma to 970 and 1, to get

970 = 1 x 970 + 0

The remainder has now become zero, so our procedure stops. Since the divisor at this stage is 1, the HCF of 1 and 970 is 1

Notice that 1 = HCF(970,1) .

HCF using Euclid's Algorithm Calculation Examples

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

Frequently Asked Questions on HCF of 990, 559, 970 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 990, 559, 970?

Answer: HCF of 990, 559, 970 is 1 the largest number that divides all the numbers leaving a remainder zero.

3. How to find HCF of 990, 559, 970 using Euclid's Algorithm?

Answer: For arbitrary numbers 990, 559, 970 apply Euclid’s Division Lemma in succession until you obtain a remainder zero. HCF is the remainder in the last but one step.