Highest Common Factor of 450, 685, 162, 603 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 450, 685, 162, 603 i.e. 1 the largest integer that leaves a remainder zero for all numbers.

HCF of 450, 685, 162, 603 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 450, 685, 162, 603 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 450, 685, 162, 603 is 1.

HCF(450, 685, 162, 603) = 1

HCF of 450, 685, 162, 603 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 450, 685, 162, 603 is 1.

Highest Common Factor of 450,685,162,603 using Euclid's algorithm

Highest Common Factor of 450,685,162,603 is 1

Step 1: Since 685 > 450, we apply the division lemma to 685 and 450, to get

685 = 450 x 1 + 235

Step 2: Since the reminder 450 ≠ 0, we apply division lemma to 235 and 450, to get

450 = 235 x 1 + 215

Step 3: We consider the new divisor 235 and the new remainder 215, and apply the division lemma to get

235 = 215 x 1 + 20

We consider the new divisor 215 and the new remainder 20,and apply the division lemma to get

215 = 20 x 10 + 15

We consider the new divisor 20 and the new remainder 15,and apply the division lemma to get

20 = 15 x 1 + 5

We consider the new divisor 15 and the new remainder 5,and apply the division lemma to get

15 = 5 x 3 + 0

The remainder has now become zero, so our procedure stops. Since the divisor at this stage is 5, the HCF of 450 and 685 is 5

Notice that 5 = HCF(15,5) = HCF(20,15) = HCF(215,20) = HCF(235,215) = HCF(450,235) = HCF(685,450) .

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

Step 1: Since 162 > 5, we apply the division lemma to 162 and 5, to get

162 = 5 x 32 + 2

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

5 = 2 x 2 + 1

Step 3: 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 162 is 1

Notice that 1 = HCF(2,1) = HCF(5,2) = HCF(162,5) .

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

Step 1: Since 603 > 1, we apply the division lemma to 603 and 1, to get

603 = 1 x 603 + 0

The remainder has now become zero, so our procedure stops. Since the divisor at this stage is 1, the HCF of 1 and 603 is 1

Notice that 1 = HCF(603,1) .

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Frequently Asked Questions on HCF of 450, 685, 162, 603 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 450, 685, 162, 603?

Answer: HCF of 450, 685, 162, 603 is 1 the largest number that divides all the numbers leaving a remainder zero.

3. How to find HCF of 450, 685, 162, 603 using Euclid's Algorithm?

Answer: For arbitrary numbers 450, 685, 162, 603 apply Euclid’s Division Lemma in succession until you obtain a remainder zero. HCF is the remainder in the last but one step.