Highest Common Factor of 5875, 2115, 29945 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 5875, 2115, 29945 i.e. 5 the largest integer that leaves a remainder zero for all numbers.

HCF of 5875, 2115, 29945 is 5 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 5875, 2115, 29945 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 5875, 2115, 29945 is 5.

HCF(5875, 2115, 29945) = 5

HCF of 5875, 2115, 29945 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 5875, 2115, 29945 is 5.

Highest Common Factor of 5875,2115,29945 using Euclid's algorithm

Highest Common Factor of 5875,2115,29945 is 5

Step 1: Since 5875 > 2115, we apply the division lemma to 5875 and 2115, to get

5875 = 2115 x 2 + 1645

Step 2: Since the reminder 2115 ≠ 0, we apply division lemma to 1645 and 2115, to get

2115 = 1645 x 1 + 470

Step 3: We consider the new divisor 1645 and the new remainder 470, and apply the division lemma to get

1645 = 470 x 3 + 235

We consider the new divisor 470 and the new remainder 235, and apply the division lemma to get

470 = 235 x 2 + 0

The remainder has now become zero, so our procedure stops. Since the divisor at this stage is 235, the HCF of 5875 and 2115 is 235

Notice that 235 = HCF(470,235) = HCF(1645,470) = HCF(2115,1645) = HCF(5875,2115) .

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

Step 1: Since 29945 > 235, we apply the division lemma to 29945 and 235, to get

29945 = 235 x 127 + 100

Step 2: Since the reminder 235 ≠ 0, we apply division lemma to 100 and 235, to get

235 = 100 x 2 + 35

Step 3: We consider the new divisor 100 and the new remainder 35, and apply the division lemma to get

100 = 35 x 2 + 30

We consider the new divisor 35 and the new remainder 30,and apply the division lemma to get

35 = 30 x 1 + 5

We consider the new divisor 30 and the new remainder 5,and apply the division lemma to get

30 = 5 x 6 + 0

The remainder has now become zero, so our procedure stops. Since the divisor at this stage is 5, the HCF of 235 and 29945 is 5

Notice that 5 = HCF(30,5) = HCF(35,30) = HCF(100,35) = HCF(235,100) = HCF(29945,235) .

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Frequently Asked Questions on HCF of 5875, 2115, 29945 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 5875, 2115, 29945?

Answer: HCF of 5875, 2115, 29945 is 5 the largest number that divides all the numbers leaving a remainder zero.

3. How to find HCF of 5875, 2115, 29945 using Euclid's Algorithm?

Answer: For arbitrary numbers 5875, 2115, 29945 apply Euclid’s Division Lemma in succession until you obtain a remainder zero. HCF is the remainder in the last but one step.