Highest Common Factor of 440, 731, 774 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, 731, 774 i.e. 1 the largest integer that leaves a remainder zero for all numbers.

HCF of 440, 731, 774 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, 731, 774 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, 731, 774 is 1.

HCF(440, 731, 774) = 1

HCF of 440, 731, 774 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, 731, 774 is 1.

Highest Common Factor of 440,731,774 using Euclid's algorithm

Highest Common Factor of 440,731,774 is 1

Step 1: Since 731 > 440, we apply the division lemma to 731 and 440, to get

731 = 440 x 1 + 291

Step 2: Since the reminder 440 ≠ 0, we apply division lemma to 291 and 440, to get

440 = 291 x 1 + 149

Step 3: We consider the new divisor 291 and the new remainder 149, and apply the division lemma to get

291 = 149 x 1 + 142

We consider the new divisor 149 and the new remainder 142,and apply the division lemma to get

149 = 142 x 1 + 7

We consider the new divisor 142 and the new remainder 7,and apply the division lemma to get

142 = 7 x 20 + 2

We consider the new divisor 7 and the new remainder 2,and apply the division lemma to get

7 = 2 x 3 + 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 731 is 1

Notice that 1 = HCF(2,1) = HCF(7,2) = HCF(142,7) = HCF(149,142) = HCF(291,149) = HCF(440,291) = HCF(731,440) .

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

Step 1: Since 774 > 1, we apply the division lemma to 774 and 1, to get

774 = 1 x 774 + 0

The remainder has now become zero, so our procedure stops. Since the divisor at this stage is 1, the HCF of 1 and 774 is 1

Notice that 1 = HCF(774,1) .

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Frequently Asked Questions on HCF of 440, 731, 774 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, 731, 774?

Answer: HCF of 440, 731, 774 is 1 the largest number that divides all the numbers leaving a remainder zero.

3. How to find HCF of 440, 731, 774 using Euclid's Algorithm?

Answer: For arbitrary numbers 440, 731, 774 apply Euclid’s Division Lemma in succession until you obtain a remainder zero. HCF is the remainder in the last but one step.