Highest Common Factor of 301, 388, 278 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 301, 388, 278 i.e. 1 the largest integer that leaves a remainder zero for all numbers.

HCF of 301, 388, 278 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 301, 388, 278 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 301, 388, 278 is 1.

HCF(301, 388, 278) = 1

HCF of 301, 388, 278 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 301, 388, 278 is 1.

Highest Common Factor of 301,388,278 using Euclid's algorithm

Highest Common Factor of 301,388,278 is 1

Step 1: Since 388 > 301, we apply the division lemma to 388 and 301, to get

388 = 301 x 1 + 87

Step 2: Since the reminder 301 ≠ 0, we apply division lemma to 87 and 301, to get

301 = 87 x 3 + 40

Step 3: We consider the new divisor 87 and the new remainder 40, and apply the division lemma to get

87 = 40 x 2 + 7

We consider the new divisor 40 and the new remainder 7,and apply the division lemma to get

40 = 7 x 5 + 5

We consider the new divisor 7 and the new remainder 5,and apply the division lemma to get

7 = 5 x 1 + 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 301 and 388 is 1

Notice that 1 = HCF(2,1) = HCF(5,2) = HCF(7,5) = HCF(40,7) = HCF(87,40) = HCF(301,87) = HCF(388,301) .

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

Step 1: Since 278 > 1, we apply the division lemma to 278 and 1, to get

278 = 1 x 278 + 0

The remainder has now become zero, so our procedure stops. Since the divisor at this stage is 1, the HCF of 1 and 278 is 1

Notice that 1 = HCF(278,1) .

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Frequently Asked Questions on HCF of 301, 388, 278 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 301, 388, 278?

Answer: HCF of 301, 388, 278 is 1 the largest number that divides all the numbers leaving a remainder zero.

3. How to find HCF of 301, 388, 278 using Euclid's Algorithm?

Answer: For arbitrary numbers 301, 388, 278 apply Euclid’s Division Lemma in succession until you obtain a remainder zero. HCF is the remainder in the last but one step.