Highest Common Factor of 873, 534, 110 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 873, 534, 110 i.e. 1 the largest integer that leaves a remainder zero for all numbers.

HCF of 873, 534, 110 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 873, 534, 110 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 873, 534, 110 is 1.

HCF(873, 534, 110) = 1

HCF of 873, 534, 110 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 873, 534, 110 is 1.

Highest Common Factor of 873,534,110 using Euclid's algorithm

Highest Common Factor of 873,534,110 is 1

Step 1: Since 873 > 534, we apply the division lemma to 873 and 534, to get

873 = 534 x 1 + 339

Step 2: Since the reminder 534 ≠ 0, we apply division lemma to 339 and 534, to get

534 = 339 x 1 + 195

Step 3: We consider the new divisor 339 and the new remainder 195, and apply the division lemma to get

339 = 195 x 1 + 144

We consider the new divisor 195 and the new remainder 144,and apply the division lemma to get

195 = 144 x 1 + 51

We consider the new divisor 144 and the new remainder 51,and apply the division lemma to get

144 = 51 x 2 + 42

We consider the new divisor 51 and the new remainder 42,and apply the division lemma to get

51 = 42 x 1 + 9

We consider the new divisor 42 and the new remainder 9,and apply the division lemma to get

42 = 9 x 4 + 6

We consider the new divisor 9 and the new remainder 6,and apply the division lemma to get

9 = 6 x 1 + 3

We consider the new divisor 6 and the new remainder 3,and apply the division lemma to get

6 = 3 x 2 + 0

The remainder has now become zero, so our procedure stops. Since the divisor at this stage is 3, the HCF of 873 and 534 is 3

Notice that 3 = HCF(6,3) = HCF(9,6) = HCF(42,9) = HCF(51,42) = HCF(144,51) = HCF(195,144) = HCF(339,195) = HCF(534,339) = HCF(873,534) .

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

Step 1: Since 110 > 3, we apply the division lemma to 110 and 3, to get

110 = 3 x 36 + 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 110 is 1

Notice that 1 = HCF(2,1) = HCF(3,2) = HCF(110,3) .

HCF using Euclid's Algorithm Calculation Examples

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

Frequently Asked Questions on HCF of 873, 534, 110 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 873, 534, 110?

Answer: HCF of 873, 534, 110 is 1 the largest number that divides all the numbers leaving a remainder zero.

3. How to find HCF of 873, 534, 110 using Euclid's Algorithm?

Answer: For arbitrary numbers 873, 534, 110 apply Euclid’s Division Lemma in succession until you obtain a remainder zero. HCF is the remainder in the last but one step.