Highest Common Factor of 461, 330, 61 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 461, 330, 61 i.e. 1 the largest integer that leaves a remainder zero for all numbers.

HCF of 461, 330, 61 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 461, 330, 61 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 461, 330, 61 is 1.

HCF(461, 330, 61) = 1

HCF of 461, 330, 61 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 461, 330, 61 is 1.

Highest Common Factor of 461,330,61 using Euclid's algorithm

Highest Common Factor of 461,330,61 is 1

Step 1: Since 461 > 330, we apply the division lemma to 461 and 330, to get

461 = 330 x 1 + 131

Step 2: Since the reminder 330 ≠ 0, we apply division lemma to 131 and 330, to get

330 = 131 x 2 + 68

Step 3: We consider the new divisor 131 and the new remainder 68, and apply the division lemma to get

131 = 68 x 1 + 63

We consider the new divisor 68 and the new remainder 63,and apply the division lemma to get

68 = 63 x 1 + 5

We consider the new divisor 63 and the new remainder 5,and apply the division lemma to get

63 = 5 x 12 + 3

We consider the new divisor 5 and the new remainder 3,and apply the division lemma to get

5 = 3 x 1 + 2

We consider the new divisor 3 and the new remainder 2,and apply the division lemma to get

3 = 2 x 1 + 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 461 and 330 is 1

Notice that 1 = HCF(2,1) = HCF(3,2) = HCF(5,3) = HCF(63,5) = HCF(68,63) = HCF(131,68) = HCF(330,131) = HCF(461,330) .

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

Step 1: Since 61 > 1, we apply the division lemma to 61 and 1, to get

61 = 1 x 61 + 0

The remainder has now become zero, so our procedure stops. Since the divisor at this stage is 1, the HCF of 1 and 61 is 1

Notice that 1 = HCF(61,1) .

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Frequently Asked Questions on HCF of 461, 330, 61 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 461, 330, 61?

Answer: HCF of 461, 330, 61 is 1 the largest number that divides all the numbers leaving a remainder zero.

3. How to find HCF of 461, 330, 61 using Euclid's Algorithm?

Answer: For arbitrary numbers 461, 330, 61 apply Euclid’s Division Lemma in succession until you obtain a remainder zero. HCF is the remainder in the last but one step.