Highest Common Factor of 561, 222, 809 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 561, 222, 809 i.e. 1 the largest integer that leaves a remainder zero for all numbers.

HCF of 561, 222, 809 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 561, 222, 809 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 561, 222, 809 is 1.

HCF(561, 222, 809) = 1

HCF of 561, 222, 809 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 561, 222, 809 is 1.

Highest Common Factor of 561,222,809 using Euclid's algorithm

Highest Common Factor of 561,222,809 is 1

Step 1: Since 561 > 222, we apply the division lemma to 561 and 222, to get

561 = 222 x 2 + 117

Step 2: Since the reminder 222 ≠ 0, we apply division lemma to 117 and 222, to get

222 = 117 x 1 + 105

Step 3: We consider the new divisor 117 and the new remainder 105, and apply the division lemma to get

117 = 105 x 1 + 12

We consider the new divisor 105 and the new remainder 12,and apply the division lemma to get

105 = 12 x 8 + 9

We consider the new divisor 12 and the new remainder 9,and apply the division lemma to get

12 = 9 x 1 + 3

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

9 = 3 x 3 + 0

The remainder has now become zero, so our procedure stops. Since the divisor at this stage is 3, the HCF of 561 and 222 is 3

Notice that 3 = HCF(9,3) = HCF(12,9) = HCF(105,12) = HCF(117,105) = HCF(222,117) = HCF(561,222) .

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

Step 1: Since 809 > 3, we apply the division lemma to 809 and 3, to get

809 = 3 x 269 + 2

Step 2: Since the reminder 3 ≠ 0, we apply division lemma to 2 and 3, to get

3 = 2 x 1 + 1

Step 3: 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 3 and 809 is 1

Notice that 1 = HCF(2,1) = HCF(3,2) = HCF(809,3) .

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Frequently Asked Questions on HCF of 561, 222, 809 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 561, 222, 809?

Answer: HCF of 561, 222, 809 is 1 the largest number that divides all the numbers leaving a remainder zero.

3. How to find HCF of 561, 222, 809 using Euclid's Algorithm?

Answer: For arbitrary numbers 561, 222, 809 apply Euclid’s Division Lemma in succession until you obtain a remainder zero. HCF is the remainder in the last but one step.