Highest Common Factor of 903, 521, 659 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 903, 521, 659 i.e. 1 the largest integer that leaves a remainder zero for all numbers.

HCF of 903, 521, 659 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 903, 521, 659 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 903, 521, 659 is 1.

HCF(903, 521, 659) = 1

HCF of 903, 521, 659 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 903, 521, 659 is 1.

Highest Common Factor of 903,521,659 using Euclid's algorithm

Highest Common Factor of 903,521,659 is 1

Step 1: Since 903 > 521, we apply the division lemma to 903 and 521, to get

903 = 521 x 1 + 382

Step 2: Since the reminder 521 ≠ 0, we apply division lemma to 382 and 521, to get

521 = 382 x 1 + 139

Step 3: We consider the new divisor 382 and the new remainder 139, and apply the division lemma to get

382 = 139 x 2 + 104

We consider the new divisor 139 and the new remainder 104,and apply the division lemma to get

139 = 104 x 1 + 35

We consider the new divisor 104 and the new remainder 35,and apply the division lemma to get

104 = 35 x 2 + 34

We consider the new divisor 35 and the new remainder 34,and apply the division lemma to get

35 = 34 x 1 + 1

We consider the new divisor 34 and the new remainder 1,and apply the division lemma to get

34 = 1 x 34 + 0

The remainder has now become zero, so our procedure stops. Since the divisor at this stage is 1, the HCF of 903 and 521 is 1

Notice that 1 = HCF(34,1) = HCF(35,34) = HCF(104,35) = HCF(139,104) = HCF(382,139) = HCF(521,382) = HCF(903,521) .

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

Step 1: Since 659 > 1, we apply the division lemma to 659 and 1, to get

659 = 1 x 659 + 0

The remainder has now become zero, so our procedure stops. Since the divisor at this stage is 1, the HCF of 1 and 659 is 1

Notice that 1 = HCF(659,1) .

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Frequently Asked Questions on HCF of 903, 521, 659 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 903, 521, 659?

Answer: HCF of 903, 521, 659 is 1 the largest number that divides all the numbers leaving a remainder zero.

3. How to find HCF of 903, 521, 659 using Euclid's Algorithm?

Answer: For arbitrary numbers 903, 521, 659 apply Euclid’s Division Lemma in succession until you obtain a remainder zero. HCF is the remainder in the last but one step.