Highest Common Factor of 635, 465, 303 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 635, 465, 303 i.e. 1 the largest integer that leaves a remainder zero for all numbers.

HCF of 635, 465, 303 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 635, 465, 303 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 635, 465, 303 is 1.

HCF(635, 465, 303) = 1

HCF of 635, 465, 303 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 635, 465, 303 is 1.

Highest Common Factor of 635,465,303 using Euclid's algorithm

Highest Common Factor of 635,465,303 is 1

Step 1: Since 635 > 465, we apply the division lemma to 635 and 465, to get

635 = 465 x 1 + 170

Step 2: Since the reminder 465 ≠ 0, we apply division lemma to 170 and 465, to get

465 = 170 x 2 + 125

Step 3: We consider the new divisor 170 and the new remainder 125, and apply the division lemma to get

170 = 125 x 1 + 45

We consider the new divisor 125 and the new remainder 45,and apply the division lemma to get

125 = 45 x 2 + 35

We consider the new divisor 45 and the new remainder 35,and apply the division lemma to get

45 = 35 x 1 + 10

We consider the new divisor 35 and the new remainder 10,and apply the division lemma to get

35 = 10 x 3 + 5

We consider the new divisor 10 and the new remainder 5,and apply the division lemma to get

10 = 5 x 2 + 0

The remainder has now become zero, so our procedure stops. Since the divisor at this stage is 5, the HCF of 635 and 465 is 5

Notice that 5 = HCF(10,5) = HCF(35,10) = HCF(45,35) = HCF(125,45) = HCF(170,125) = HCF(465,170) = HCF(635,465) .

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

Step 1: Since 303 > 5, we apply the division lemma to 303 and 5, to get

303 = 5 x 60 + 3

Step 2: Since the reminder 5 ≠ 0, we apply division lemma to 3 and 5, to get

5 = 3 x 1 + 2

Step 3: We consider the new divisor 3 and the new remainder 2, and apply the division lemma to get

3 = 2 x 1 + 1

We consider the new divisor 2 and the new remainder 1, and apply the division lemma to get

2 = 1 x 2 + 0

The remainder has now become zero, so our procedure stops. Since the divisor at this stage is 1, the HCF of 5 and 303 is 1

Notice that 1 = HCF(2,1) = HCF(3,2) = HCF(5,3) = HCF(303,5) .

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Frequently Asked Questions on HCF of 635, 465, 303 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 635, 465, 303?

Answer: HCF of 635, 465, 303 is 1 the largest number that divides all the numbers leaving a remainder zero.

3. How to find HCF of 635, 465, 303 using Euclid's Algorithm?

Answer: For arbitrary numbers 635, 465, 303 apply Euclid’s Division Lemma in succession until you obtain a remainder zero. HCF is the remainder in the last but one step.