Highest Common Factor of 673, 914, 665, 45 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 673, 914, 665, 45 i.e. 1 the largest integer that leaves a remainder zero for all numbers.

HCF of 673, 914, 665, 45 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 673, 914, 665, 45 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 673, 914, 665, 45 is 1.

HCF(673, 914, 665, 45) = 1

HCF of 673, 914, 665, 45 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 673, 914, 665, 45 is 1.

Highest Common Factor of 673,914,665,45 using Euclid's algorithm

Highest Common Factor of 673,914,665,45 is 1

Step 1: Since 914 > 673, we apply the division lemma to 914 and 673, to get

914 = 673 x 1 + 241

Step 2: Since the reminder 673 ≠ 0, we apply division lemma to 241 and 673, to get

673 = 241 x 2 + 191

Step 3: We consider the new divisor 241 and the new remainder 191, and apply the division lemma to get

241 = 191 x 1 + 50

We consider the new divisor 191 and the new remainder 50,and apply the division lemma to get

191 = 50 x 3 + 41

We consider the new divisor 50 and the new remainder 41,and apply the division lemma to get

50 = 41 x 1 + 9

We consider the new divisor 41 and the new remainder 9,and apply the division lemma to get

41 = 9 x 4 + 5

We consider the new divisor 9 and the new remainder 5,and apply the division lemma to get

9 = 5 x 1 + 4

We consider the new divisor 5 and the new remainder 4,and apply the division lemma to get

5 = 4 x 1 + 1

We consider the new divisor 4 and the new remainder 1,and apply the division lemma to get

4 = 1 x 4 + 0

The remainder has now become zero, so our procedure stops. Since the divisor at this stage is 1, the HCF of 673 and 914 is 1

Notice that 1 = HCF(4,1) = HCF(5,4) = HCF(9,5) = HCF(41,9) = HCF(50,41) = HCF(191,50) = HCF(241,191) = HCF(673,241) = HCF(914,673) .

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

Step 1: Since 665 > 1, we apply the division lemma to 665 and 1, to get

665 = 1 x 665 + 0

The remainder has now become zero, so our procedure stops. Since the divisor at this stage is 1, the HCF of 1 and 665 is 1

Notice that 1 = HCF(665,1) .

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

Step 1: Since 45 > 1, we apply the division lemma to 45 and 1, to get

45 = 1 x 45 + 0

The remainder has now become zero, so our procedure stops. Since the divisor at this stage is 1, the HCF of 1 and 45 is 1

Notice that 1 = HCF(45,1) .

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Frequently Asked Questions on HCF of 673, 914, 665, 45 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 673, 914, 665, 45?

Answer: HCF of 673, 914, 665, 45 is 1 the largest number that divides all the numbers leaving a remainder zero.

3. How to find HCF of 673, 914, 665, 45 using Euclid's Algorithm?

Answer: For arbitrary numbers 673, 914, 665, 45 apply Euclid’s Division Lemma in succession until you obtain a remainder zero. HCF is the remainder in the last but one step.