Highest Common Factor of 909, 508, 101 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 909, 508, 101 i.e. 1 the largest integer that leaves a remainder zero for all numbers.

HCF of 909, 508, 101 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 909, 508, 101 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 909, 508, 101 is 1.

HCF(909, 508, 101) = 1

HCF of 909, 508, 101 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 909, 508, 101 is 1.

Highest Common Factor of 909,508,101 using Euclid's algorithm

Highest Common Factor of 909,508,101 is 1

Step 1: Since 909 > 508, we apply the division lemma to 909 and 508, to get

909 = 508 x 1 + 401

Step 2: Since the reminder 508 ≠ 0, we apply division lemma to 401 and 508, to get

508 = 401 x 1 + 107

Step 3: We consider the new divisor 401 and the new remainder 107, and apply the division lemma to get

401 = 107 x 3 + 80

We consider the new divisor 107 and the new remainder 80,and apply the division lemma to get

107 = 80 x 1 + 27

We consider the new divisor 80 and the new remainder 27,and apply the division lemma to get

80 = 27 x 2 + 26

We consider the new divisor 27 and the new remainder 26,and apply the division lemma to get

27 = 26 x 1 + 1

We consider the new divisor 26 and the new remainder 1,and apply the division lemma to get

26 = 1 x 26 + 0

The remainder has now become zero, so our procedure stops. Since the divisor at this stage is 1, the HCF of 909 and 508 is 1

Notice that 1 = HCF(26,1) = HCF(27,26) = HCF(80,27) = HCF(107,80) = HCF(401,107) = HCF(508,401) = HCF(909,508) .

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

Step 1: Since 101 > 1, we apply the division lemma to 101 and 1, to get

101 = 1 x 101 + 0

The remainder has now become zero, so our procedure stops. Since the divisor at this stage is 1, the HCF of 1 and 101 is 1

Notice that 1 = HCF(101,1) .

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Frequently Asked Questions on HCF of 909, 508, 101 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 909, 508, 101?

Answer: HCF of 909, 508, 101 is 1 the largest number that divides all the numbers leaving a remainder zero.

3. How to find HCF of 909, 508, 101 using Euclid's Algorithm?

Answer: For arbitrary numbers 909, 508, 101 apply Euclid’s Division Lemma in succession until you obtain a remainder zero. HCF is the remainder in the last but one step.