Highest Common Factor of 827, 373, 745 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 827, 373, 745 i.e. 1 the largest integer that leaves a remainder zero for all numbers.

HCF of 827, 373, 745 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 827, 373, 745 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 827, 373, 745 is 1.

HCF(827, 373, 745) = 1

HCF of 827, 373, 745 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 827, 373, 745 is 1.

Highest Common Factor of 827,373,745 using Euclid's algorithm

Highest Common Factor of 827,373,745 is 1

Step 1: Since 827 > 373, we apply the division lemma to 827 and 373, to get

827 = 373 x 2 + 81

Step 2: Since the reminder 373 ≠ 0, we apply division lemma to 81 and 373, to get

373 = 81 x 4 + 49

Step 3: We consider the new divisor 81 and the new remainder 49, and apply the division lemma to get

81 = 49 x 1 + 32

We consider the new divisor 49 and the new remainder 32,and apply the division lemma to get

49 = 32 x 1 + 17

We consider the new divisor 32 and the new remainder 17,and apply the division lemma to get

32 = 17 x 1 + 15

We consider the new divisor 17 and the new remainder 15,and apply the division lemma to get

17 = 15 x 1 + 2

We consider the new divisor 15 and the new remainder 2,and apply the division lemma to get

15 = 2 x 7 + 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 827 and 373 is 1

Notice that 1 = HCF(2,1) = HCF(15,2) = HCF(17,15) = HCF(32,17) = HCF(49,32) = HCF(81,49) = HCF(373,81) = HCF(827,373) .

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) .

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Frequently Asked Questions on HCF of 827, 373, 745 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 827, 373, 745?

Answer: HCF of 827, 373, 745 is 1 the largest number that divides all the numbers leaving a remainder zero.

3. How to find HCF of 827, 373, 745 using Euclid's Algorithm?

Answer: For arbitrary numbers 827, 373, 745 apply Euclid’s Division Lemma in succession until you obtain a remainder zero. HCF is the remainder in the last but one step.