Highest Common Factor of 402, 225, 652 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 402, 225, 652 i.e. 1 the largest integer that leaves a remainder zero for all numbers.

HCF of 402, 225, 652 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 402, 225, 652 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 402, 225, 652 is 1.

HCF(402, 225, 652) = 1

HCF of 402, 225, 652 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 402, 225, 652 is 1.

Highest Common Factor of 402,225,652 using Euclid's algorithm

Highest Common Factor of 402,225,652 is 1

Step 1: Since 402 > 225, we apply the division lemma to 402 and 225, to get

402 = 225 x 1 + 177

Step 2: Since the reminder 225 ≠ 0, we apply division lemma to 177 and 225, to get

225 = 177 x 1 + 48

Step 3: We consider the new divisor 177 and the new remainder 48, and apply the division lemma to get

177 = 48 x 3 + 33

We consider the new divisor 48 and the new remainder 33,and apply the division lemma to get

48 = 33 x 1 + 15

We consider the new divisor 33 and the new remainder 15,and apply the division lemma to get

33 = 15 x 2 + 3

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

15 = 3 x 5 + 0

The remainder has now become zero, so our procedure stops. Since the divisor at this stage is 3, the HCF of 402 and 225 is 3

Notice that 3 = HCF(15,3) = HCF(33,15) = HCF(48,33) = HCF(177,48) = HCF(225,177) = HCF(402,225) .

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

Step 1: Since 652 > 3, we apply the division lemma to 652 and 3, to get

652 = 3 x 217 + 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 652 is 1

Notice that 1 = HCF(3,1) = HCF(652,3) .

HCF using Euclid's Algorithm Calculation Examples

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

Frequently Asked Questions on HCF of 402, 225, 652 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 402, 225, 652?

Answer: HCF of 402, 225, 652 is 1 the largest number that divides all the numbers leaving a remainder zero.

3. How to find HCF of 402, 225, 652 using Euclid's Algorithm?

Answer: For arbitrary numbers 402, 225, 652 apply Euclid’s Division Lemma in succession until you obtain a remainder zero. HCF is the remainder in the last but one step.