Highest Common Factor of 288, 374, 342 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 288, 374, 342 i.e. 2 the largest integer that leaves a remainder zero for all numbers.

HCF of 288, 374, 342 is 2 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 288, 374, 342 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 288, 374, 342 is 2.

HCF(288, 374, 342) = 2

HCF of 288, 374, 342 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 288, 374, 342 is 2.

Highest Common Factor of 288,374,342 using Euclid's algorithm

Highest Common Factor of 288,374,342 is 2

Step 1: Since 374 > 288, we apply the division lemma to 374 and 288, to get

374 = 288 x 1 + 86

Step 2: Since the reminder 288 ≠ 0, we apply division lemma to 86 and 288, to get

288 = 86 x 3 + 30

Step 3: We consider the new divisor 86 and the new remainder 30, and apply the division lemma to get

86 = 30 x 2 + 26

We consider the new divisor 30 and the new remainder 26,and apply the division lemma to get

30 = 26 x 1 + 4

We consider the new divisor 26 and the new remainder 4,and apply the division lemma to get

26 = 4 x 6 + 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 288 and 374 is 2

Notice that 2 = HCF(4,2) = HCF(26,4) = HCF(30,26) = HCF(86,30) = HCF(288,86) = HCF(374,288) .

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

Step 1: Since 342 > 2, we apply the division lemma to 342 and 2, to get

342 = 2 x 171 + 0

The remainder has now become zero, so our procedure stops. Since the divisor at this stage is 2, the HCF of 2 and 342 is 2

Notice that 2 = HCF(342,2) .

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Frequently Asked Questions on HCF of 288, 374, 342 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 288, 374, 342?

Answer: HCF of 288, 374, 342 is 2 the largest number that divides all the numbers leaving a remainder zero.

3. How to find HCF of 288, 374, 342 using Euclid's Algorithm?

Answer: For arbitrary numbers 288, 374, 342 apply Euclid’s Division Lemma in succession until you obtain a remainder zero. HCF is the remainder in the last but one step.