Highest Common Factor of 75, 45, 251 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 75, 45, 251 i.e. 1 the largest integer that leaves a remainder zero for all numbers.

HCF of 75, 45, 251 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 75, 45, 251 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 75, 45, 251 is 1.

HCF(75, 45, 251) = 1

HCF of 75, 45, 251 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 75, 45, 251 is 1.

Highest Common Factor of 75,45,251 using Euclid's algorithm

Highest Common Factor of 75,45,251 is 1

Step 1: Since 75 > 45, we apply the division lemma to 75 and 45, to get

75 = 45 x 1 + 30

Step 2: Since the reminder 45 ≠ 0, we apply division lemma to 30 and 45, to get

45 = 30 x 1 + 15

Step 3: We consider the new divisor 30 and the new remainder 15, and apply the division lemma to get

30 = 15 x 2 + 0

The remainder has now become zero, so our procedure stops. Since the divisor at this stage is 15, the HCF of 75 and 45 is 15

Notice that 15 = HCF(30,15) = HCF(45,30) = HCF(75,45) .

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

Step 1: Since 251 > 15, we apply the division lemma to 251 and 15, to get

251 = 15 x 16 + 11

Step 2: Since the reminder 15 ≠ 0, we apply division lemma to 11 and 15, to get

15 = 11 x 1 + 4

Step 3: 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 15 and 251 is 1

Notice that 1 = HCF(3,1) = HCF(4,3) = HCF(11,4) = HCF(15,11) = HCF(251,15) .

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Frequently Asked Questions on HCF of 75, 45, 251 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 75, 45, 251?

Answer: HCF of 75, 45, 251 is 1 the largest number that divides all the numbers leaving a remainder zero.

3. How to find HCF of 75, 45, 251 using Euclid's Algorithm?

Answer: For arbitrary numbers 75, 45, 251 apply Euclid’s Division Lemma in succession until you obtain a remainder zero. HCF is the remainder in the last but one step.