Highest Common Factor of 278, 821, 375 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 278, 821, 375 i.e. 1 the largest integer that leaves a remainder zero for all numbers.

HCF of 278, 821, 375 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 278, 821, 375 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 278, 821, 375 is 1.

HCF(278, 821, 375) = 1

HCF of 278, 821, 375 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 278, 821, 375 is 1.

Highest Common Factor of 278,821,375 using Euclid's algorithm

Highest Common Factor of 278,821,375 is 1

Step 1: Since 821 > 278, we apply the division lemma to 821 and 278, to get

821 = 278 x 2 + 265

Step 2: Since the reminder 278 ≠ 0, we apply division lemma to 265 and 278, to get

278 = 265 x 1 + 13

Step 3: We consider the new divisor 265 and the new remainder 13, and apply the division lemma to get

265 = 13 x 20 + 5

We consider the new divisor 13 and the new remainder 5,and apply the division lemma to get

13 = 5 x 2 + 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 278 and 821 is 1

Notice that 1 = HCF(2,1) = HCF(3,2) = HCF(5,3) = HCF(13,5) = HCF(265,13) = HCF(278,265) = HCF(821,278) .

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

Step 1: Since 375 > 1, we apply the division lemma to 375 and 1, to get

375 = 1 x 375 + 0

The remainder has now become zero, so our procedure stops. Since the divisor at this stage is 1, the HCF of 1 and 375 is 1

Notice that 1 = HCF(375,1) .

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Frequently Asked Questions on HCF of 278, 821, 375 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 278, 821, 375?

Answer: HCF of 278, 821, 375 is 1 the largest number that divides all the numbers leaving a remainder zero.

3. How to find HCF of 278, 821, 375 using Euclid's Algorithm?

Answer: For arbitrary numbers 278, 821, 375 apply Euclid’s Division Lemma in succession until you obtain a remainder zero. HCF is the remainder in the last but one step.