Highest Common Factor of 561, 777, 199 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, 777, 199 i.e. 1 the largest integer that leaves a remainder zero for all numbers.

HCF of 561, 777, 199 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, 777, 199 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, 777, 199 is 1.

HCF(561, 777, 199) = 1

HCF of 561, 777, 199 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, 777, 199 is 1.

Highest Common Factor of 561,777,199 using Euclid's algorithm

Highest Common Factor of 561,777,199 is 1

Step 1: Since 777 > 561, we apply the division lemma to 777 and 561, to get

777 = 561 x 1 + 216

Step 2: Since the reminder 561 ≠ 0, we apply division lemma to 216 and 561, to get

561 = 216 x 2 + 129

Step 3: We consider the new divisor 216 and the new remainder 129, and apply the division lemma to get

216 = 129 x 1 + 87

We consider the new divisor 129 and the new remainder 87,and apply the division lemma to get

129 = 87 x 1 + 42

We consider the new divisor 87 and the new remainder 42,and apply the division lemma to get

87 = 42 x 2 + 3

We consider the new divisor 42 and the new remainder 3,and apply the division lemma to get

42 = 3 x 14 + 0

The remainder has now become zero, so our procedure stops. Since the divisor at this stage is 3, the HCF of 561 and 777 is 3

Notice that 3 = HCF(42,3) = HCF(87,42) = HCF(129,87) = HCF(216,129) = HCF(561,216) = HCF(777,561) .

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

Step 1: Since 199 > 3, we apply the division lemma to 199 and 3, to get

199 = 3 x 66 + 1

Step 2: Since the reminder 3 ≠ 0, we apply division lemma to 1 and 3, to get

3 = 1 x 3 + 0

The remainder has now become zero, so our procedure stops. Since the divisor at this stage is 1, the HCF of 3 and 199 is 1

Notice that 1 = HCF(3,1) = HCF(199,3) .

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Frequently Asked Questions on HCF of 561, 777, 199 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, 777, 199?

Answer: HCF of 561, 777, 199 is 1 the largest number that divides all the numbers leaving a remainder zero.

3. How to find HCF of 561, 777, 199 using Euclid's Algorithm?

Answer: For arbitrary numbers 561, 777, 199 apply Euclid’s Division Lemma in succession until you obtain a remainder zero. HCF is the remainder in the last but one step.