Highest Common Factor of 559, 906, 880 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 559, 906, 880 i.e. 1 the largest integer that leaves a remainder zero for all numbers.

HCF of 559, 906, 880 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 559, 906, 880 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 559, 906, 880 is 1.

HCF(559, 906, 880) = 1

HCF of 559, 906, 880 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 559, 906, 880 is 1.

Highest Common Factor of 559,906,880 using Euclid's algorithm

Highest Common Factor of 559,906,880 is 1

Step 1: Since 906 > 559, we apply the division lemma to 906 and 559, to get

906 = 559 x 1 + 347

Step 2: Since the reminder 559 ≠ 0, we apply division lemma to 347 and 559, to get

559 = 347 x 1 + 212

Step 3: We consider the new divisor 347 and the new remainder 212, and apply the division lemma to get

347 = 212 x 1 + 135

We consider the new divisor 212 and the new remainder 135,and apply the division lemma to get

212 = 135 x 1 + 77

We consider the new divisor 135 and the new remainder 77,and apply the division lemma to get

135 = 77 x 1 + 58

We consider the new divisor 77 and the new remainder 58,and apply the division lemma to get

77 = 58 x 1 + 19

We consider the new divisor 58 and the new remainder 19,and apply the division lemma to get

58 = 19 x 3 + 1

We consider the new divisor 19 and the new remainder 1,and apply the division lemma to get

19 = 1 x 19 + 0

The remainder has now become zero, so our procedure stops. Since the divisor at this stage is 1, the HCF of 559 and 906 is 1

Notice that 1 = HCF(19,1) = HCF(58,19) = HCF(77,58) = HCF(135,77) = HCF(212,135) = HCF(347,212) = HCF(559,347) = HCF(906,559) .

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

Step 1: Since 880 > 1, we apply the division lemma to 880 and 1, to get

880 = 1 x 880 + 0

The remainder has now become zero, so our procedure stops. Since the divisor at this stage is 1, the HCF of 1 and 880 is 1

Notice that 1 = HCF(880,1) .

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Frequently Asked Questions on HCF of 559, 906, 880 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 559, 906, 880?

Answer: HCF of 559, 906, 880 is 1 the largest number that divides all the numbers leaving a remainder zero.

3. How to find HCF of 559, 906, 880 using Euclid's Algorithm?

Answer: For arbitrary numbers 559, 906, 880 apply Euclid’s Division Lemma in succession until you obtain a remainder zero. HCF is the remainder in the last but one step.