Highest Common Factor of 221, 559, 100 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 221, 559, 100 i.e. 1 the largest integer that leaves a remainder zero for all numbers.

HCF of 221, 559, 100 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 221, 559, 100 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 221, 559, 100 is 1.

HCF(221, 559, 100) = 1

HCF of 221, 559, 100 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 221, 559, 100 is 1.

Highest Common Factor of 221,559,100 using Euclid's algorithm

Highest Common Factor of 221,559,100 is 1

Step 1: Since 559 > 221, we apply the division lemma to 559 and 221, to get

559 = 221 x 2 + 117

Step 2: Since the reminder 221 ≠ 0, we apply division lemma to 117 and 221, to get

221 = 117 x 1 + 104

Step 3: We consider the new divisor 117 and the new remainder 104, and apply the division lemma to get

117 = 104 x 1 + 13

We consider the new divisor 104 and the new remainder 13, and apply the division lemma to get

104 = 13 x 8 + 0

The remainder has now become zero, so our procedure stops. Since the divisor at this stage is 13, the HCF of 221 and 559 is 13

Notice that 13 = HCF(104,13) = HCF(117,104) = HCF(221,117) = HCF(559,221) .

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

Step 1: Since 100 > 13, we apply the division lemma to 100 and 13, to get

100 = 13 x 7 + 9

Step 2: Since the reminder 13 ≠ 0, we apply division lemma to 9 and 13, to get

13 = 9 x 1 + 4

Step 3: We consider the new divisor 9 and the new remainder 4, and apply the division lemma to get

9 = 4 x 2 + 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 13 and 100 is 1

Notice that 1 = HCF(4,1) = HCF(9,4) = HCF(13,9) = HCF(100,13) .

HCF using Euclid's Algorithm Calculation Examples

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

Frequently Asked Questions on HCF of 221, 559, 100 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 221, 559, 100?

Answer: HCF of 221, 559, 100 is 1 the largest number that divides all the numbers leaving a remainder zero.

3. How to find HCF of 221, 559, 100 using Euclid's Algorithm?

Answer: For arbitrary numbers 221, 559, 100 apply Euclid’s Division Lemma in succession until you obtain a remainder zero. HCF is the remainder in the last but one step.