Highest Common Factor of 440, 669, 440 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 440, 669, 440 i.e. 1 the largest integer that leaves a remainder zero for all numbers.

HCF of 440, 669, 440 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 440, 669, 440 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 440, 669, 440 is 1.

HCF(440, 669, 440) = 1

HCF of 440, 669, 440 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 440, 669, 440 is 1.

Highest Common Factor of 440,669,440 using Euclid's algorithm

Highest Common Factor of 440,669,440 is 1

Step 1: Since 669 > 440, we apply the division lemma to 669 and 440, to get

669 = 440 x 1 + 229

Step 2: Since the reminder 440 ≠ 0, we apply division lemma to 229 and 440, to get

440 = 229 x 1 + 211

Step 3: We consider the new divisor 229 and the new remainder 211, and apply the division lemma to get

229 = 211 x 1 + 18

We consider the new divisor 211 and the new remainder 18,and apply the division lemma to get

211 = 18 x 11 + 13

We consider the new divisor 18 and the new remainder 13,and apply the division lemma to get

18 = 13 x 1 + 5

We consider the new divisor 13 and the new remainder 5,and apply the division lemma to get

13 = 5 x 2 + 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 440 and 669 is 1

Notice that 1 = HCF(2,1) = HCF(3,2) = HCF(5,3) = HCF(13,5) = HCF(18,13) = HCF(211,18) = HCF(229,211) = HCF(440,229) = HCF(669,440) .

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

Step 1: Since 440 > 1, we apply the division lemma to 440 and 1, to get

440 = 1 x 440 + 0

The remainder has now become zero, so our procedure stops. Since the divisor at this stage is 1, the HCF of 1 and 440 is 1

Notice that 1 = HCF(440,1) .

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Frequently Asked Questions on HCF of 440, 669, 440 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 440, 669, 440?

Answer: HCF of 440, 669, 440 is 1 the largest number that divides all the numbers leaving a remainder zero.

3. How to find HCF of 440, 669, 440 using Euclid's Algorithm?

Answer: For arbitrary numbers 440, 669, 440 apply Euclid’s Division Lemma in succession until you obtain a remainder zero. HCF is the remainder in the last but one step.