Highest Common Factor of 161, 310, 147 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 161, 310, 147 i.e. 1 the largest integer that leaves a remainder zero for all numbers.

HCF of 161, 310, 147 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 161, 310, 147 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 161, 310, 147 is 1.

HCF(161, 310, 147) = 1

HCF of 161, 310, 147 using Euclid's algorithm

Highest common factor or Highest common divisor (hcd) can be calculated by Euclid's algotithm.

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Highest common factor (HCF) of 161, 310, 147 is 1.

Highest Common Factor of 161,310,147 using Euclid's algorithm

Highest Common Factor of 161,310,147 is 1

Step 1: Since 310 > 161, we apply the division lemma to 310 and 161, to get

310 = 161 x 1 + 149

Step 2: Since the reminder 161 ≠ 0, we apply division lemma to 149 and 161, to get

161 = 149 x 1 + 12

Step 3: We consider the new divisor 149 and the new remainder 12, and apply the division lemma to get

149 = 12 x 12 + 5

We consider the new divisor 12 and the new remainder 5,and apply the division lemma to get

12 = 5 x 2 + 2

We consider the new divisor 5 and the new remainder 2,and apply the division lemma to get

5 = 2 x 2 + 1

We consider the new divisor 2 and the new remainder 1,and apply the division lemma 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 161 and 310 is 1

Notice that 1 = HCF(2,1) = HCF(5,2) = HCF(12,5) = HCF(149,12) = HCF(161,149) = HCF(310,161) .

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

Step 1: Since 147 > 1, we apply the division lemma to 147 and 1, to get

147 = 1 x 147 + 0

The remainder has now become zero, so our procedure stops. Since the divisor at this stage is 1, the HCF of 1 and 147 is 1

Notice that 1 = HCF(147,1) .

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Frequently Asked Questions on HCF of 161, 310, 147 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 161, 310, 147?

Answer: HCF of 161, 310, 147 is 1 the largest number that divides all the numbers leaving a remainder zero.

3. How to find HCF of 161, 310, 147 using Euclid's Algorithm?

Answer: For arbitrary numbers 161, 310, 147 apply Euclid’s Division Lemma in succession until you obtain a remainder zero. HCF is the remainder in the last but one step.