Highest Common Factor of 449, 720, 400 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 449, 720, 400 i.e. 1 the largest integer that leaves a remainder zero for all numbers.

HCF of 449, 720, 400 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 449, 720, 400 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 449, 720, 400 is 1.

HCF(449, 720, 400) = 1

HCF of 449, 720, 400 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 449, 720, 400 is 1.

Highest Common Factor of 449,720,400 using Euclid's algorithm

Highest Common Factor of 449,720,400 is 1

Step 1: Since 720 > 449, we apply the division lemma to 720 and 449, to get

720 = 449 x 1 + 271

Step 2: Since the reminder 449 ≠ 0, we apply division lemma to 271 and 449, to get

449 = 271 x 1 + 178

Step 3: We consider the new divisor 271 and the new remainder 178, and apply the division lemma to get

271 = 178 x 1 + 93

We consider the new divisor 178 and the new remainder 93,and apply the division lemma to get

178 = 93 x 1 + 85

We consider the new divisor 93 and the new remainder 85,and apply the division lemma to get

93 = 85 x 1 + 8

We consider the new divisor 85 and the new remainder 8,and apply the division lemma to get

85 = 8 x 10 + 5

We consider the new divisor 8 and the new remainder 5,and apply the division lemma to get

8 = 5 x 1 + 3

We consider the new divisor 5 and the new remainder 3,and apply the division lemma to get

5 = 3 x 1 + 2

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 449 and 720 is 1

Notice that 1 = HCF(2,1) = HCF(3,2) = HCF(5,3) = HCF(8,5) = HCF(85,8) = HCF(93,85) = HCF(178,93) = HCF(271,178) = HCF(449,271) = HCF(720,449) .

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

Step 1: Since 400 > 1, we apply the division lemma to 400 and 1, to get

400 = 1 x 400 + 0

The remainder has now become zero, so our procedure stops. Since the divisor at this stage is 1, the HCF of 1 and 400 is 1

Notice that 1 = HCF(400,1) .

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Frequently Asked Questions on HCF of 449, 720, 400 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 449, 720, 400?

Answer: HCF of 449, 720, 400 is 1 the largest number that divides all the numbers leaving a remainder zero.

3. How to find HCF of 449, 720, 400 using Euclid's Algorithm?

Answer: For arbitrary numbers 449, 720, 400 apply Euclid’s Division Lemma in succession until you obtain a remainder zero. HCF is the remainder in the last but one step.