Highest Common Factor of 674, 365, 960, 896 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, 365, 960, 896 i.e. 1 the largest integer that leaves a remainder zero for all numbers.

HCF of 674, 365, 960, 896 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 674, 365, 960, 896 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, 365, 960, 896 is 1.

HCF(674, 365, 960, 896) = 1

HCF of 674, 365, 960, 896 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, 365, 960, 896 is 1.

Highest Common Factor of 674,365,960,896 using Euclid's algorithm

Highest Common Factor of 674,365,960,896 is 1

Step 1: Since 674 > 365, we apply the division lemma to 674 and 365, to get

674 = 365 x 1 + 309

Step 2: Since the reminder 365 ≠ 0, we apply division lemma to 309 and 365, to get

365 = 309 x 1 + 56

Step 3: We consider the new divisor 309 and the new remainder 56, and apply the division lemma to get

309 = 56 x 5 + 29

We consider the new divisor 56 and the new remainder 29,and apply the division lemma to get

56 = 29 x 1 + 27

We consider the new divisor 29 and the new remainder 27,and apply the division lemma to get

29 = 27 x 1 + 2

We consider the new divisor 27 and the new remainder 2,and apply the division lemma to get

27 = 2 x 13 + 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 674 and 365 is 1

Notice that 1 = HCF(2,1) = HCF(27,2) = HCF(29,27) = HCF(56,29) = HCF(309,56) = HCF(365,309) = HCF(674,365) .

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

Step 1: Since 960 > 1, we apply the division lemma to 960 and 1, to get

960 = 1 x 960 + 0

The remainder has now become zero, so our procedure stops. Since the divisor at this stage is 1, the HCF of 1 and 960 is 1

Notice that 1 = HCF(960,1) .

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

Step 1: Since 896 > 1, we apply the division lemma to 896 and 1, to get

896 = 1 x 896 + 0

The remainder has now become zero, so our procedure stops. Since the divisor at this stage is 1, the HCF of 1 and 896 is 1

Notice that 1 = HCF(896,1) .

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Frequently Asked Questions on HCF of 674, 365, 960, 896 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, 365, 960, 896?

Answer: HCF of 674, 365, 960, 896 is 1 the largest number that divides all the numbers leaving a remainder zero.

3. How to find HCF of 674, 365, 960, 896 using Euclid's Algorithm?

Answer: For arbitrary numbers 674, 365, 960, 896 apply Euclid’s Division Lemma in succession until you obtain a remainder zero. HCF is the remainder in the last but one step.