Highest Common Factor of 909, 310, 161 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, 310, 161 i.e. 1 the largest integer that leaves a remainder zero for all numbers.

HCF of 909, 310, 161 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, 310, 161 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, 310, 161 is 1.

HCF(909, 310, 161) = 1

HCF of 909, 310, 161 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, 310, 161 is 1.

Highest Common Factor of 909,310,161 using Euclid's algorithm

Highest Common Factor of 909,310,161 is 1

Step 1: Since 909 > 310, we apply the division lemma to 909 and 310, to get

909 = 310 x 2 + 289

Step 2: Since the reminder 310 ≠ 0, we apply division lemma to 289 and 310, to get

310 = 289 x 1 + 21

Step 3: We consider the new divisor 289 and the new remainder 21, and apply the division lemma to get

289 = 21 x 13 + 16

We consider the new divisor 21 and the new remainder 16,and apply the division lemma to get

21 = 16 x 1 + 5

We consider the new divisor 16 and the new remainder 5,and apply the division lemma to get

16 = 5 x 3 + 1

We consider the new divisor 5 and the new remainder 1,and apply the division lemma to get

5 = 1 x 5 + 0

The remainder has now become zero, so our procedure stops. Since the divisor at this stage is 1, the HCF of 909 and 310 is 1

Notice that 1 = HCF(5,1) = HCF(16,5) = HCF(21,16) = HCF(289,21) = HCF(310,289) = HCF(909,310) .

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

Step 1: Since 161 > 1, we apply the division lemma to 161 and 1, to get

161 = 1 x 161 + 0

The remainder has now become zero, so our procedure stops. Since the divisor at this stage is 1, the HCF of 1 and 161 is 1

Notice that 1 = HCF(161,1) .

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Frequently Asked Questions on HCF of 909, 310, 161 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, 310, 161?

Answer: HCF of 909, 310, 161 is 1 the largest number that divides all the numbers leaving a remainder zero.

3. How to find HCF of 909, 310, 161 using Euclid's Algorithm?

Answer: For arbitrary numbers 909, 310, 161 apply Euclid’s Division Lemma in succession until you obtain a remainder zero. HCF is the remainder in the last but one step.