Highest Common Factor of 878, 552, 13 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 878, 552, 13 i.e. 1 the largest integer that leaves a remainder zero for all numbers.

HCF of 878, 552, 13 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 878, 552, 13 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 878, 552, 13 is 1.

HCF(878, 552, 13) = 1

HCF of 878, 552, 13 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 878, 552, 13 is 1.

Highest Common Factor of 878,552,13 using Euclid's algorithm

Highest Common Factor of 878,552,13 is 1

Step 1: Since 878 > 552, we apply the division lemma to 878 and 552, to get

878 = 552 x 1 + 326

Step 2: Since the reminder 552 ≠ 0, we apply division lemma to 326 and 552, to get

552 = 326 x 1 + 226

Step 3: We consider the new divisor 326 and the new remainder 226, and apply the division lemma to get

326 = 226 x 1 + 100

We consider the new divisor 226 and the new remainder 100,and apply the division lemma to get

226 = 100 x 2 + 26

We consider the new divisor 100 and the new remainder 26,and apply the division lemma to get

100 = 26 x 3 + 22

We consider the new divisor 26 and the new remainder 22,and apply the division lemma to get

26 = 22 x 1 + 4

We consider the new divisor 22 and the new remainder 4,and apply the division lemma to get

22 = 4 x 5 + 2

We consider the new divisor 4 and the new remainder 2,and apply the division lemma to get

4 = 2 x 2 + 0

The remainder has now become zero, so our procedure stops. Since the divisor at this stage is 2, the HCF of 878 and 552 is 2

Notice that 2 = HCF(4,2) = HCF(22,4) = HCF(26,22) = HCF(100,26) = HCF(226,100) = HCF(326,226) = HCF(552,326) = HCF(878,552) .

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

Step 1: Since 13 > 2, we apply the division lemma to 13 and 2, to get

13 = 2 x 6 + 1

Step 2: Since the reminder 2 ≠ 0, we apply division lemma to 1 and 2, 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 2 and 13 is 1

Notice that 1 = HCF(2,1) = HCF(13,2) .

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Frequently Asked Questions on HCF of 878, 552, 13 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 878, 552, 13?

Answer: HCF of 878, 552, 13 is 1 the largest number that divides all the numbers leaving a remainder zero.

3. How to find HCF of 878, 552, 13 using Euclid's Algorithm?

Answer: For arbitrary numbers 878, 552, 13 apply Euclid’s Division Lemma in succession until you obtain a remainder zero. HCF is the remainder in the last but one step.