Highest Common Factor of 388, 278, 703 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 388, 278, 703 i.e. 1 the largest integer that leaves a remainder zero for all numbers.

HCF of 388, 278, 703 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 388, 278, 703 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 388, 278, 703 is 1.

HCF(388, 278, 703) = 1

HCF of 388, 278, 703 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 388, 278, 703 is 1.

Highest Common Factor of 388,278,703 using Euclid's algorithm

Highest Common Factor of 388,278,703 is 1

Step 1: Since 388 > 278, we apply the division lemma to 388 and 278, to get

388 = 278 x 1 + 110

Step 2: Since the reminder 278 ≠ 0, we apply division lemma to 110 and 278, to get

278 = 110 x 2 + 58

Step 3: We consider the new divisor 110 and the new remainder 58, and apply the division lemma to get

110 = 58 x 1 + 52

We consider the new divisor 58 and the new remainder 52,and apply the division lemma to get

58 = 52 x 1 + 6

We consider the new divisor 52 and the new remainder 6,and apply the division lemma to get

52 = 6 x 8 + 4

We consider the new divisor 6 and the new remainder 4,and apply the division lemma to get

6 = 4 x 1 + 2

We consider the new divisor 4 and the new remainder 2,and apply the division lemma to get

4 = 2 x 2 + 0

The remainder has now become zero, so our procedure stops. Since the divisor at this stage is 2, the HCF of 388 and 278 is 2

Notice that 2 = HCF(4,2) = HCF(6,4) = HCF(52,6) = HCF(58,52) = HCF(110,58) = HCF(278,110) = HCF(388,278) .

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

Step 1: Since 703 > 2, we apply the division lemma to 703 and 2, to get

703 = 2 x 351 + 1

Step 2: Since the reminder 2 ≠ 0, we apply division lemma to 1 and 2, 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 2 and 703 is 1

Notice that 1 = HCF(2,1) = HCF(703,2) .

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Frequently Asked Questions on HCF of 388, 278, 703 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 388, 278, 703?

Answer: HCF of 388, 278, 703 is 1 the largest number that divides all the numbers leaving a remainder zero.

3. How to find HCF of 388, 278, 703 using Euclid's Algorithm?

Answer: For arbitrary numbers 388, 278, 703 apply Euclid’s Division Lemma in succession until you obtain a remainder zero. HCF is the remainder in the last but one step.