Highest Common Factor of 745, 289 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, 289 i.e. 1 the largest integer that leaves a remainder zero for all numbers.

HCF of 745, 289 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, 289 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, 289 is 1.

HCF(745, 289) = 1

HCF of 745, 289 using Euclid's algorithm

Highest common factor or Highest common divisor (hcd) can be calculated by Euclid's algotithm.

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Highest common factor (HCF) of 745, 289 is 1.

Highest Common Factor of 745,289 using Euclid's algorithm

Highest Common Factor of 745,289 is 1

Step 1: Since 745 > 289, we apply the division lemma to 745 and 289, to get

745 = 289 x 2 + 167

Step 2: Since the reminder 289 ≠ 0, we apply division lemma to 167 and 289, to get

289 = 167 x 1 + 122

Step 3: We consider the new divisor 167 and the new remainder 122, and apply the division lemma to get

167 = 122 x 1 + 45

We consider the new divisor 122 and the new remainder 45,and apply the division lemma to get

122 = 45 x 2 + 32

We consider the new divisor 45 and the new remainder 32,and apply the division lemma to get

45 = 32 x 1 + 13

We consider the new divisor 32 and the new remainder 13,and apply the division lemma to get

32 = 13 x 2 + 6

We consider the new divisor 13 and the new remainder 6,and apply the division lemma to get

13 = 6 x 2 + 1

We consider the new divisor 6 and the new remainder 1,and apply the division lemma to get

6 = 1 x 6 + 0

The remainder has now become zero, so our procedure stops. Since the divisor at this stage is 1, the HCF of 745 and 289 is 1

Notice that 1 = HCF(6,1) = HCF(13,6) = HCF(32,13) = HCF(45,32) = HCF(122,45) = HCF(167,122) = HCF(289,167) = HCF(745,289) .

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Frequently Asked Questions on HCF of 745, 289 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, 289?

Answer: HCF of 745, 289 is 1 the largest number that divides all the numbers leaving a remainder zero.

3. How to find HCF of 745, 289 using Euclid's Algorithm?

Answer: For arbitrary numbers 745, 289 apply Euclid’s Division Lemma in succession until you obtain a remainder zero. HCF is the remainder in the last but one step.