Highest Common Factor of 334, 460, 380 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 334, 460, 380 i.e. 2 the largest integer that leaves a remainder zero for all numbers.

HCF of 334, 460, 380 is 2 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 334, 460, 380 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 334, 460, 380 is 2.

HCF(334, 460, 380) = 2

HCF of 334, 460, 380 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 334, 460, 380 is 2.

Highest Common Factor of 334,460,380 using Euclid's algorithm

Highest Common Factor of 334,460,380 is 2

Step 1: Since 460 > 334, we apply the division lemma to 460 and 334, to get

460 = 334 x 1 + 126

Step 2: Since the reminder 334 ≠ 0, we apply division lemma to 126 and 334, to get

334 = 126 x 2 + 82

Step 3: We consider the new divisor 126 and the new remainder 82, and apply the division lemma to get

126 = 82 x 1 + 44

We consider the new divisor 82 and the new remainder 44,and apply the division lemma to get

82 = 44 x 1 + 38

We consider the new divisor 44 and the new remainder 38,and apply the division lemma to get

44 = 38 x 1 + 6

We consider the new divisor 38 and the new remainder 6,and apply the division lemma to get

38 = 6 x 6 + 2

We consider the new divisor 6 and the new remainder 2,and apply the division lemma to get

6 = 2 x 3 + 0

The remainder has now become zero, so our procedure stops. Since the divisor at this stage is 2, the HCF of 334 and 460 is 2

Notice that 2 = HCF(6,2) = HCF(38,6) = HCF(44,38) = HCF(82,44) = HCF(126,82) = HCF(334,126) = HCF(460,334) .

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

Step 1: Since 380 > 2, we apply the division lemma to 380 and 2, to get

380 = 2 x 190 + 0

The remainder has now become zero, so our procedure stops. Since the divisor at this stage is 2, the HCF of 2 and 380 is 2

Notice that 2 = HCF(380,2) .

HCF using Euclid's Algorithm Calculation Examples

Here are some samples of HCF using Euclid's Algorithm calculations.

Frequently Asked Questions on HCF of 334, 460, 380 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 334, 460, 380?

Answer: HCF of 334, 460, 380 is 2 the largest number that divides all the numbers leaving a remainder zero.

3. How to find HCF of 334, 460, 380 using Euclid's Algorithm?

Answer: For arbitrary numbers 334, 460, 380 apply Euclid’s Division Lemma in succession until you obtain a remainder zero. HCF is the remainder in the last but one step.