Highest Common Factor of 365, 563, 745, 34 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 365, 563, 745, 34 i.e. 1 the largest integer that leaves a remainder zero for all numbers.

HCF of 365, 563, 745, 34 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 365, 563, 745, 34 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 365, 563, 745, 34 is 1.

HCF(365, 563, 745, 34) = 1

HCF of 365, 563, 745, 34 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 365, 563, 745, 34 is 1.

Highest Common Factor of 365,563,745,34 using Euclid's algorithm

Highest Common Factor of 365,563,745,34 is 1

Step 1: Since 563 > 365, we apply the division lemma to 563 and 365, to get

563 = 365 x 1 + 198

Step 2: Since the reminder 365 ≠ 0, we apply division lemma to 198 and 365, to get

365 = 198 x 1 + 167

Step 3: We consider the new divisor 198 and the new remainder 167, and apply the division lemma to get

198 = 167 x 1 + 31

We consider the new divisor 167 and the new remainder 31,and apply the division lemma to get

167 = 31 x 5 + 12

We consider the new divisor 31 and the new remainder 12,and apply the division lemma to get

31 = 12 x 2 + 7

We consider the new divisor 12 and the new remainder 7,and apply the division lemma to get

12 = 7 x 1 + 5

We consider the new divisor 7 and the new remainder 5,and apply the division lemma to get

7 = 5 x 1 + 2

We consider the new divisor 5 and the new remainder 2,and apply the division lemma to get

5 = 2 x 2 + 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 365 and 563 is 1

Notice that 1 = HCF(2,1) = HCF(5,2) = HCF(7,5) = HCF(12,7) = HCF(31,12) = HCF(167,31) = HCF(198,167) = HCF(365,198) = HCF(563,365) .

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

Step 1: Since 745 > 1, we apply the division lemma to 745 and 1, to get

745 = 1 x 745 + 0

The remainder has now become zero, so our procedure stops. Since the divisor at this stage is 1, the HCF of 1 and 745 is 1

Notice that 1 = HCF(745,1) .

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

Step 1: Since 34 > 1, we apply the division lemma to 34 and 1, to get

34 = 1 x 34 + 0

The remainder has now become zero, so our procedure stops. Since the divisor at this stage is 1, the HCF of 1 and 34 is 1

Notice that 1 = HCF(34,1) .

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Frequently Asked Questions on HCF of 365, 563, 745, 34 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 365, 563, 745, 34?

Answer: HCF of 365, 563, 745, 34 is 1 the largest number that divides all the numbers leaving a remainder zero.

3. How to find HCF of 365, 563, 745, 34 using Euclid's Algorithm?

Answer: For arbitrary numbers 365, 563, 745, 34 apply Euclid’s Division Lemma in succession until you obtain a remainder zero. HCF is the remainder in the last but one step.