Highest Common Factor of 745, 66822 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 745, 66822 i.e. 1 the largest integer that leaves a remainder zero for all numbers.

HCF of 745, 66822 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 745, 66822 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 745, 66822 is 1.

HCF(745, 66822) = 1

HCF of 745, 66822 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 745, 66822 is 1.

Highest Common Factor of 745,66822 using Euclid's algorithm

Highest Common Factor of 745,66822 is 1

Step 1: Since 66822 > 745, we apply the division lemma to 66822 and 745, to get

66822 = 745 x 89 + 517

Step 2: Since the reminder 745 ≠ 0, we apply division lemma to 517 and 745, to get

745 = 517 x 1 + 228

Step 3: We consider the new divisor 517 and the new remainder 228, and apply the division lemma to get

517 = 228 x 2 + 61

We consider the new divisor 228 and the new remainder 61,and apply the division lemma to get

228 = 61 x 3 + 45

We consider the new divisor 61 and the new remainder 45,and apply the division lemma to get

61 = 45 x 1 + 16

We consider the new divisor 45 and the new remainder 16,and apply the division lemma to get

45 = 16 x 2 + 13

We consider the new divisor 16 and the new remainder 13,and apply the division lemma to get

16 = 13 x 1 + 3

We consider the new divisor 13 and the new remainder 3,and apply the division lemma to get

13 = 3 x 4 + 1

We consider the new divisor 3 and the new remainder 1,and apply the division lemma to get

3 = 1 x 3 + 0

The remainder has now become zero, so our procedure stops. Since the divisor at this stage is 1, the HCF of 745 and 66822 is 1

Notice that 1 = HCF(3,1) = HCF(13,3) = HCF(16,13) = HCF(45,16) = HCF(61,45) = HCF(228,61) = HCF(517,228) = HCF(745,517) = HCF(66822,745) .

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Frequently Asked Questions on HCF of 745, 66822 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 745, 66822?

Answer: HCF of 745, 66822 is 1 the largest number that divides all the numbers leaving a remainder zero.

3. How to find HCF of 745, 66822 using Euclid's Algorithm?

Answer: For arbitrary numbers 745, 66822 apply Euclid’s Division Lemma in succession until you obtain a remainder zero. HCF is the remainder in the last but one step.