Highest Common Factor of 725, 990, 450 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 725, 990, 450 i.e. 5 the largest integer that leaves a remainder zero for all numbers.

HCF of 725, 990, 450 is 5 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 725, 990, 450 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 725, 990, 450 is 5.

HCF(725, 990, 450) = 5

HCF of 725, 990, 450 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 725, 990, 450 is 5.

Highest Common Factor of 725,990,450 using Euclid's algorithm

Highest Common Factor of 725,990,450 is 5

Step 1: Since 990 > 725, we apply the division lemma to 990 and 725, to get

990 = 725 x 1 + 265

Step 2: Since the reminder 725 ≠ 0, we apply division lemma to 265 and 725, to get

725 = 265 x 2 + 195

Step 3: We consider the new divisor 265 and the new remainder 195, and apply the division lemma to get

265 = 195 x 1 + 70

We consider the new divisor 195 and the new remainder 70,and apply the division lemma to get

195 = 70 x 2 + 55

We consider the new divisor 70 and the new remainder 55,and apply the division lemma to get

70 = 55 x 1 + 15

We consider the new divisor 55 and the new remainder 15,and apply the division lemma to get

55 = 15 x 3 + 10

We consider the new divisor 15 and the new remainder 10,and apply the division lemma to get

15 = 10 x 1 + 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 725 and 990 is 5

Notice that 5 = HCF(10,5) = HCF(15,10) = HCF(55,15) = HCF(70,55) = HCF(195,70) = HCF(265,195) = HCF(725,265) = HCF(990,725) .

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

Step 1: Since 450 > 5, we apply the division lemma to 450 and 5, to get

450 = 5 x 90 + 0

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

Notice that 5 = HCF(450,5) .

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Frequently Asked Questions on HCF of 725, 990, 450 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 725, 990, 450?

Answer: HCF of 725, 990, 450 is 5 the largest number that divides all the numbers leaving a remainder zero.

3. How to find HCF of 725, 990, 450 using Euclid's Algorithm?

Answer: For arbitrary numbers 725, 990, 450 apply Euclid’s Division Lemma in succession until you obtain a remainder zero. HCF is the remainder in the last but one step.