Highest Common Factor of 561, 369, 88 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, 369, 88 i.e. 1 the largest integer that leaves a remainder zero for all numbers.

HCF of 561, 369, 88 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, 369, 88 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, 369, 88 is 1.

HCF(561, 369, 88) = 1

HCF of 561, 369, 88 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, 369, 88 is 1.

Highest Common Factor of 561,369,88 using Euclid's algorithm

Highest Common Factor of 561,369,88 is 1

Step 1: Since 561 > 369, we apply the division lemma to 561 and 369, to get

561 = 369 x 1 + 192

Step 2: Since the reminder 369 ≠ 0, we apply division lemma to 192 and 369, to get

369 = 192 x 1 + 177

Step 3: We consider the new divisor 192 and the new remainder 177, and apply the division lemma to get

192 = 177 x 1 + 15

We consider the new divisor 177 and the new remainder 15,and apply the division lemma to get

177 = 15 x 11 + 12

We consider the new divisor 15 and the new remainder 12,and apply the division lemma to get

15 = 12 x 1 + 3

We consider the new divisor 12 and the new remainder 3,and apply the division lemma to get

12 = 3 x 4 + 0

The remainder has now become zero, so our procedure stops. Since the divisor at this stage is 3, the HCF of 561 and 369 is 3

Notice that 3 = HCF(12,3) = HCF(15,12) = HCF(177,15) = HCF(192,177) = HCF(369,192) = HCF(561,369) .

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

Step 1: Since 88 > 3, we apply the division lemma to 88 and 3, to get

88 = 3 x 29 + 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 88 is 1

Notice that 1 = HCF(3,1) = HCF(88,3) .

HCF using Euclid's Algorithm Calculation Examples

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

Frequently Asked Questions on HCF of 561, 369, 88 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, 369, 88?

Answer: HCF of 561, 369, 88 is 1 the largest number that divides all the numbers leaving a remainder zero.

3. How to find HCF of 561, 369, 88 using Euclid's Algorithm?

Answer: For arbitrary numbers 561, 369, 88 apply Euclid’s Division Lemma in succession until you obtain a remainder zero. HCF is the remainder in the last but one step.