Highest Common Factor of 301, 475, 278, 245 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, 475, 278, 245 i.e. 1 the largest integer that leaves a remainder zero for all numbers.

HCF of 301, 475, 278, 245 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, 475, 278, 245 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, 475, 278, 245 is 1.

HCF(301, 475, 278, 245) = 1

HCF of 301, 475, 278, 245 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, 475, 278, 245 is 1.

Highest Common Factor of 301,475,278,245 using Euclid's algorithm

Highest Common Factor of 301,475,278,245 is 1

Step 1: Since 475 > 301, we apply the division lemma to 475 and 301, to get

475 = 301 x 1 + 174

Step 2: Since the reminder 301 ≠ 0, we apply division lemma to 174 and 301, to get

301 = 174 x 1 + 127

Step 3: We consider the new divisor 174 and the new remainder 127, and apply the division lemma to get

174 = 127 x 1 + 47

We consider the new divisor 127 and the new remainder 47,and apply the division lemma to get

127 = 47 x 2 + 33

We consider the new divisor 47 and the new remainder 33,and apply the division lemma to get

47 = 33 x 1 + 14

We consider the new divisor 33 and the new remainder 14,and apply the division lemma to get

33 = 14 x 2 + 5

We consider the new divisor 14 and the new remainder 5,and apply the division lemma to get

14 = 5 x 2 + 4

We consider the new divisor 5 and the new remainder 4,and apply the division lemma to get

5 = 4 x 1 + 1

We consider the new divisor 4 and the new remainder 1,and apply the division lemma to get

4 = 1 x 4 + 0

The remainder has now become zero, so our procedure stops. Since the divisor at this stage is 1, the HCF of 301 and 475 is 1

Notice that 1 = HCF(4,1) = HCF(5,4) = HCF(14,5) = HCF(33,14) = HCF(47,33) = HCF(127,47) = HCF(174,127) = HCF(301,174) = HCF(475,301) .

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) .

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

Step 1: Since 245 > 1, we apply the division lemma to 245 and 1, to get

245 = 1 x 245 + 0

The remainder has now become zero, so our procedure stops. Since the divisor at this stage is 1, the HCF of 1 and 245 is 1

Notice that 1 = HCF(245,1) .

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Frequently Asked Questions on HCF of 301, 475, 278, 245 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, 475, 278, 245?

Answer: HCF of 301, 475, 278, 245 is 1 the largest number that divides all the numbers leaving a remainder zero.

3. How to find HCF of 301, 475, 278, 245 using Euclid's Algorithm?

Answer: For arbitrary numbers 301, 475, 278, 245 apply Euclid’s Division Lemma in succession until you obtain a remainder zero. HCF is the remainder in the last but one step.