Highest Common Factor of 286, 750, 351 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 286, 750, 351 i.e. 1 the largest integer that leaves a remainder zero for all numbers.

HCF of 286, 750, 351 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 286, 750, 351 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 286, 750, 351 is 1.

HCF(286, 750, 351) = 1

HCF of 286, 750, 351 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 286, 750, 351 is 1.

Highest Common Factor of 286,750,351 using Euclid's algorithm

Highest Common Factor of 286,750,351 is 1

Step 1: Since 750 > 286, we apply the division lemma to 750 and 286, to get

750 = 286 x 2 + 178

Step 2: Since the reminder 286 ≠ 0, we apply division lemma to 178 and 286, to get

286 = 178 x 1 + 108

Step 3: We consider the new divisor 178 and the new remainder 108, and apply the division lemma to get

178 = 108 x 1 + 70

We consider the new divisor 108 and the new remainder 70,and apply the division lemma to get

108 = 70 x 1 + 38

We consider the new divisor 70 and the new remainder 38,and apply the division lemma to get

70 = 38 x 1 + 32

We consider the new divisor 38 and the new remainder 32,and apply the division lemma to get

38 = 32 x 1 + 6

We consider the new divisor 32 and the new remainder 6,and apply the division lemma to get

32 = 6 x 5 + 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 286 and 750 is 2

Notice that 2 = HCF(6,2) = HCF(32,6) = HCF(38,32) = HCF(70,38) = HCF(108,70) = HCF(178,108) = HCF(286,178) = HCF(750,286) .

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

Step 1: Since 351 > 2, we apply the division lemma to 351 and 2, to get

351 = 2 x 175 + 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 351 is 1

Notice that 1 = HCF(2,1) = HCF(351,2) .

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Frequently Asked Questions on HCF of 286, 750, 351 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 286, 750, 351?

Answer: HCF of 286, 750, 351 is 1 the largest number that divides all the numbers leaving a remainder zero.

3. How to find HCF of 286, 750, 351 using Euclid's Algorithm?

Answer: For arbitrary numbers 286, 750, 351 apply Euclid’s Division Lemma in succession until you obtain a remainder zero. HCF is the remainder in the last but one step.