Highest Common Factor of 745, 712 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, 712 i.e. 1 the largest integer that leaves a remainder zero for all numbers.

HCF of 745, 712 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, 712 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, 712 is 1.

HCF(745, 712) = 1

HCF of 745, 712 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, 712 is 1.

Highest Common Factor of 745,712 using Euclid's algorithm

Highest Common Factor of 745,712 is 1

Step 1: Since 745 > 712, we apply the division lemma to 745 and 712, to get

745 = 712 x 1 + 33

Step 2: Since the reminder 712 ≠ 0, we apply division lemma to 33 and 712, to get

712 = 33 x 21 + 19

Step 3: We consider the new divisor 33 and the new remainder 19, and apply the division lemma to get

33 = 19 x 1 + 14

We consider the new divisor 19 and the new remainder 14,and apply the division lemma to get

19 = 14 x 1 + 5

We consider the new divisor 14 and the new remainder 5,and apply the division lemma to get

14 = 5 x 2 + 4

We consider the new divisor 5 and the new remainder 4,and apply the division lemma to get

5 = 4 x 1 + 1

We consider the new divisor 4 and the new remainder 1,and apply the division lemma to get

4 = 1 x 4 + 0

The remainder has now become zero, so our procedure stops. Since the divisor at this stage is 1, the HCF of 745 and 712 is 1

Notice that 1 = HCF(4,1) = HCF(5,4) = HCF(14,5) = HCF(19,14) = HCF(33,19) = HCF(712,33) = HCF(745,712) .

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Frequently Asked Questions on HCF of 745, 712 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, 712?

Answer: HCF of 745, 712 is 1 the largest number that divides all the numbers leaving a remainder zero.

3. How to find HCF of 745, 712 using Euclid's Algorithm?

Answer: For arbitrary numbers 745, 712 apply Euclid’s Division Lemma in succession until you obtain a remainder zero. HCF is the remainder in the last but one step.