Highest Common Factor of 216, 990, 365, 83 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 216, 990, 365, 83 i.e. 1 the largest integer that leaves a remainder zero for all numbers.

HCF of 216, 990, 365, 83 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 216, 990, 365, 83 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 216, 990, 365, 83 is 1.

HCF(216, 990, 365, 83) = 1

HCF of 216, 990, 365, 83 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 216, 990, 365, 83 is 1.

Highest Common Factor of 216,990,365,83 using Euclid's algorithm

Highest Common Factor of 216,990,365,83 is 1

Step 1: Since 990 > 216, we apply the division lemma to 990 and 216, to get

990 = 216 x 4 + 126

Step 2: Since the reminder 216 ≠ 0, we apply division lemma to 126 and 216, to get

216 = 126 x 1 + 90

Step 3: We consider the new divisor 126 and the new remainder 90, and apply the division lemma to get

126 = 90 x 1 + 36

We consider the new divisor 90 and the new remainder 36,and apply the division lemma to get

90 = 36 x 2 + 18

We consider the new divisor 36 and the new remainder 18,and apply the division lemma to get

36 = 18 x 2 + 0

The remainder has now become zero, so our procedure stops. Since the divisor at this stage is 18, the HCF of 216 and 990 is 18

Notice that 18 = HCF(36,18) = HCF(90,36) = HCF(126,90) = HCF(216,126) = HCF(990,216) .

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

Step 1: Since 365 > 18, we apply the division lemma to 365 and 18, to get

365 = 18 x 20 + 5

Step 2: Since the reminder 18 ≠ 0, we apply division lemma to 5 and 18, to get

18 = 5 x 3 + 3

Step 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 18 and 365 is 1

Notice that 1 = HCF(2,1) = HCF(3,2) = HCF(5,3) = HCF(18,5) = HCF(365,18) .

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

Step 1: Since 83 > 1, we apply the division lemma to 83 and 1, to get

83 = 1 x 83 + 0

The remainder has now become zero, so our procedure stops. Since the divisor at this stage is 1, the HCF of 1 and 83 is 1

Notice that 1 = HCF(83,1) .

HCF using Euclid's Algorithm Calculation Examples

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

Frequently Asked Questions on HCF of 216, 990, 365, 83 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 216, 990, 365, 83?

Answer: HCF of 216, 990, 365, 83 is 1 the largest number that divides all the numbers leaving a remainder zero.

3. How to find HCF of 216, 990, 365, 83 using Euclid's Algorithm?

Answer: For arbitrary numbers 216, 990, 365, 83 apply Euclid’s Division Lemma in succession until you obtain a remainder zero. HCF is the remainder in the last but one step.