Highest Common Factor of 75, 423, 952 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, 423, 952 i.e. 1 the largest integer that leaves a remainder zero for all numbers.

HCF of 75, 423, 952 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, 423, 952 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, 423, 952 is 1.

HCF(75, 423, 952) = 1

HCF of 75, 423, 952 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, 423, 952 is 1.

Highest Common Factor of 75,423,952 using Euclid's algorithm

Highest Common Factor of 75,423,952 is 1

Step 1: Since 423 > 75, we apply the division lemma to 423 and 75, to get

423 = 75 x 5 + 48

Step 2: Since the reminder 75 ≠ 0, we apply division lemma to 48 and 75, to get

75 = 48 x 1 + 27

Step 3: We consider the new divisor 48 and the new remainder 27, and apply the division lemma to get

48 = 27 x 1 + 21

We consider the new divisor 27 and the new remainder 21,and apply the division lemma to get

27 = 21 x 1 + 6

We consider the new divisor 21 and the new remainder 6,and apply the division lemma to get

21 = 6 x 3 + 3

We consider the new divisor 6 and the new remainder 3,and apply the division lemma to get

6 = 3 x 2 + 0

The remainder has now become zero, so our procedure stops. Since the divisor at this stage is 3, the HCF of 75 and 423 is 3

Notice that 3 = HCF(6,3) = HCF(21,6) = HCF(27,21) = HCF(48,27) = HCF(75,48) = HCF(423,75) .

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

Step 1: Since 952 > 3, we apply the division lemma to 952 and 3, to get

952 = 3 x 317 + 1

Step 2: Since the reminder 3 ≠ 0, we apply division lemma to 1 and 3, 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 3 and 952 is 1

Notice that 1 = HCF(3,1) = HCF(952,3) .

HCF using Euclid's Algorithm Calculation Examples

Here are some samples of HCF using Euclid's Algorithm calculations.

Frequently Asked Questions on HCF of 75, 423, 952 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, 423, 952?

Answer: HCF of 75, 423, 952 is 1 the largest number that divides all the numbers leaving a remainder zero.

3. How to find HCF of 75, 423, 952 using Euclid's Algorithm?

Answer: For arbitrary numbers 75, 423, 952 apply Euclid’s Division Lemma in succession until you obtain a remainder zero. HCF is the remainder in the last but one step.