Highest Common Factor of 456, 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 456, 745 i.e. 1 the largest integer that leaves a remainder zero for all numbers.

HCF of 456, 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 456, 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 456, 745 is 1.

HCF(456, 745) = 1

HCF of 456, 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 456, 745 is 1.

Highest Common Factor of 456,745 using Euclid's algorithm

Highest Common Factor of 456,745 is 1

Step 1: Since 745 > 456, we apply the division lemma to 745 and 456, to get

745 = 456 x 1 + 289

Step 2: Since the reminder 456 ≠ 0, we apply division lemma to 289 and 456, to get

456 = 289 x 1 + 167

Step 3: We consider the new divisor 289 and the new remainder 167, and apply the division lemma to get

289 = 167 x 1 + 122

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 456 and 745 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(456,289) = HCF(745,456) .

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Frequently Asked Questions on HCF of 456, 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 456, 745?

Answer: HCF of 456, 745 is 1 the largest number that divides all the numbers leaving a remainder zero.

3. How to find HCF of 456, 745 using Euclid's Algorithm?

Answer: For arbitrary numbers 456, 745 apply Euclid’s Division Lemma in succession until you obtain a remainder zero. HCF is the remainder in the last but one step.