Highest Common Factor of 288, 475, 120 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, 475, 120 i.e. 1 the largest integer that leaves a remainder zero for all numbers.

HCF of 288, 475, 120 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 288, 475, 120 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, 475, 120 is 1.

HCF(288, 475, 120) = 1

HCF of 288, 475, 120 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, 475, 120 is 1.

Highest Common Factor of 288,475,120 using Euclid's algorithm

Highest Common Factor of 288,475,120 is 1

Step 1: Since 475 > 288, we apply the division lemma to 475 and 288, to get

475 = 288 x 1 + 187

Step 2: Since the reminder 288 ≠ 0, we apply division lemma to 187 and 288, to get

288 = 187 x 1 + 101

Step 3: We consider the new divisor 187 and the new remainder 101, and apply the division lemma to get

187 = 101 x 1 + 86

We consider the new divisor 101 and the new remainder 86,and apply the division lemma to get

101 = 86 x 1 + 15

We consider the new divisor 86 and the new remainder 15,and apply the division lemma to get

86 = 15 x 5 + 11

We consider the new divisor 15 and the new remainder 11,and apply the division lemma to get

15 = 11 x 1 + 4

We consider the new divisor 11 and the new remainder 4,and apply the division lemma to get

11 = 4 x 2 + 3

We consider the new divisor 4 and the new remainder 3,and apply the division lemma to get

4 = 3 x 1 + 1

We consider the new divisor 3 and the new remainder 1,and apply the division lemma to get

3 = 1 x 3 + 0

The remainder has now become zero, so our procedure stops. Since the divisor at this stage is 1, the HCF of 288 and 475 is 1

Notice that 1 = HCF(3,1) = HCF(4,3) = HCF(11,4) = HCF(15,11) = HCF(86,15) = HCF(101,86) = HCF(187,101) = HCF(288,187) = HCF(475,288) .

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

Step 1: Since 120 > 1, we apply the division lemma to 120 and 1, to get

120 = 1 x 120 + 0

The remainder has now become zero, so our procedure stops. Since the divisor at this stage is 1, the HCF of 1 and 120 is 1

Notice that 1 = HCF(120,1) .

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Frequently Asked Questions on HCF of 288, 475, 120 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, 475, 120?

Answer: HCF of 288, 475, 120 is 1 the largest number that divides all the numbers leaving a remainder zero.

3. How to find HCF of 288, 475, 120 using Euclid's Algorithm?

Answer: For arbitrary numbers 288, 475, 120 apply Euclid’s Division Lemma in succession until you obtain a remainder zero. HCF is the remainder in the last but one step.