Highest Common Factor of 41, 67, 30 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 41, 67, 30 i.e. 1 the largest integer that leaves a remainder zero for all numbers.

HCF of 41, 67, 30 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 41, 67, 30 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 41, 67, 30 is 1.

HCF(41, 67, 30) = 1

HCF of 41, 67, 30 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 41, 67, 30 is 1.

Highest Common Factor of 41,67,30 using Euclid's algorithm

Highest Common Factor of 41,67,30 is 1

Step 1: Since 67 > 41, we apply the division lemma to 67 and 41, to get

67 = 41 x 1 + 26

Step 2: Since the reminder 41 ≠ 0, we apply division lemma to 26 and 41, to get

41 = 26 x 1 + 15

Step 3: We consider the new divisor 26 and the new remainder 15, and apply the division lemma to get

26 = 15 x 1 + 11

We consider the new divisor 15 and the new remainder 11,and apply the division lemma to get

15 = 11 x 1 + 4

We consider the new divisor 11 and the new remainder 4,and apply the division lemma to get

11 = 4 x 2 + 3

We consider the new divisor 4 and the new remainder 3,and apply the division lemma to get

4 = 3 x 1 + 1

We consider the new divisor 3 and the new remainder 1,and apply the division lemma to get

3 = 1 x 3 + 0

The remainder has now become zero, so our procedure stops. Since the divisor at this stage is 1, the HCF of 41 and 67 is 1

Notice that 1 = HCF(3,1) = HCF(4,3) = HCF(11,4) = HCF(15,11) = HCF(26,15) = HCF(41,26) = HCF(67,41) .

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

Step 1: Since 30 > 1, we apply the division lemma to 30 and 1, to get

30 = 1 x 30 + 0

The remainder has now become zero, so our procedure stops. Since the divisor at this stage is 1, the HCF of 1 and 30 is 1

Notice that 1 = HCF(30,1) .

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Frequently Asked Questions on HCF of 41, 67, 30 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 41, 67, 30?

Answer: HCF of 41, 67, 30 is 1 the largest number that divides all the numbers leaving a remainder zero.

3. How to find HCF of 41, 67, 30 using Euclid's Algorithm?

Answer: For arbitrary numbers 41, 67, 30 apply Euclid’s Division Lemma in succession until you obtain a remainder zero. HCF is the remainder in the last but one step.