Highest Common Factor of 450, 735, 703 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, 735, 703 i.e. 1 the largest integer that leaves a remainder zero for all numbers.

HCF of 450, 735, 703 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, 735, 703 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, 735, 703 is 1.

HCF(450, 735, 703) = 1

HCF of 450, 735, 703 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, 735, 703 is 1.

Highest Common Factor of 450,735,703 using Euclid's algorithm

Highest Common Factor of 450,735,703 is 1

Step 1: Since 735 > 450, we apply the division lemma to 735 and 450, to get

735 = 450 x 1 + 285

Step 2: Since the reminder 450 ≠ 0, we apply division lemma to 285 and 450, to get

450 = 285 x 1 + 165

Step 3: We consider the new divisor 285 and the new remainder 165, and apply the division lemma to get

285 = 165 x 1 + 120

We consider the new divisor 165 and the new remainder 120,and apply the division lemma to get

165 = 120 x 1 + 45

We consider the new divisor 120 and the new remainder 45,and apply the division lemma to get

120 = 45 x 2 + 30

We consider the new divisor 45 and the new remainder 30,and apply the division lemma to get

45 = 30 x 1 + 15

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 450 and 735 is 15

Notice that 15 = HCF(30,15) = HCF(45,30) = HCF(120,45) = HCF(165,120) = HCF(285,165) = HCF(450,285) = HCF(735,450) .

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

Step 1: Since 703 > 15, we apply the division lemma to 703 and 15, to get

703 = 15 x 46 + 13

Step 2: Since the reminder 15 ≠ 0, we apply division lemma to 13 and 15, to get

15 = 13 x 1 + 2

Step 3: We consider the new divisor 13 and the new remainder 2, and apply the division lemma to get

13 = 2 x 6 + 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 15 and 703 is 1

Notice that 1 = HCF(2,1) = HCF(13,2) = HCF(15,13) = HCF(703,15) .

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Frequently Asked Questions on HCF of 450, 735, 703 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, 735, 703?

Answer: HCF of 450, 735, 703 is 1 the largest number that divides all the numbers leaving a remainder zero.

3. How to find HCF of 450, 735, 703 using Euclid's Algorithm?

Answer: For arbitrary numbers 450, 735, 703 apply Euclid’s Division Lemma in succession until you obtain a remainder zero. HCF is the remainder in the last but one step.