Highest Common Factor of 674, 240, 744 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 674, 240, 744 i.e. 2 the largest integer that leaves a remainder zero for all numbers.

HCF of 674, 240, 744 is 2 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 674, 240, 744 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 674, 240, 744 is 2.

HCF(674, 240, 744) = 2

HCF of 674, 240, 744 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 674, 240, 744 is 2.

Highest Common Factor of 674,240,744 using Euclid's algorithm

Highest Common Factor of 674,240,744 is 2

Step 1: Since 674 > 240, we apply the division lemma to 674 and 240, to get

674 = 240 x 2 + 194

Step 2: Since the reminder 240 ≠ 0, we apply division lemma to 194 and 240, to get

240 = 194 x 1 + 46

Step 3: We consider the new divisor 194 and the new remainder 46, and apply the division lemma to get

194 = 46 x 4 + 10

We consider the new divisor 46 and the new remainder 10,and apply the division lemma to get

46 = 10 x 4 + 6

We consider the new divisor 10 and the new remainder 6,and apply the division lemma to get

10 = 6 x 1 + 4

We consider the new divisor 6 and the new remainder 4,and apply the division lemma to get

6 = 4 x 1 + 2

We consider the new divisor 4 and the new remainder 2,and apply the division lemma to get

4 = 2 x 2 + 0

The remainder has now become zero, so our procedure stops. Since the divisor at this stage is 2, the HCF of 674 and 240 is 2

Notice that 2 = HCF(4,2) = HCF(6,4) = HCF(10,6) = HCF(46,10) = HCF(194,46) = HCF(240,194) = HCF(674,240) .

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

Step 1: Since 744 > 2, we apply the division lemma to 744 and 2, to get

744 = 2 x 372 + 0

The remainder has now become zero, so our procedure stops. Since the divisor at this stage is 2, the HCF of 2 and 744 is 2

Notice that 2 = HCF(744,2) .

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Frequently Asked Questions on HCF of 674, 240, 744 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 674, 240, 744?

Answer: HCF of 674, 240, 744 is 2 the largest number that divides all the numbers leaving a remainder zero.

3. How to find HCF of 674, 240, 744 using Euclid's Algorithm?

Answer: For arbitrary numbers 674, 240, 744 apply Euclid’s Division Lemma in succession until you obtain a remainder zero. HCF is the remainder in the last but one step.