Highest Common Factor of 752, 287 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 752, 287 i.e. 1 the largest integer that leaves a remainder zero for all numbers.

HCF of 752, 287 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 752, 287 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 752, 287 is 1.

HCF(752, 287) = 1

HCF of 752, 287 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 752, 287 is 1.

Highest Common Factor of 752,287 using Euclid's algorithm

Highest Common Factor of 752,287 is 1

Step 1: Since 752 > 287, we apply the division lemma to 752 and 287, to get

752 = 287 x 2 + 178

Step 2: Since the reminder 287 ≠ 0, we apply division lemma to 178 and 287, to get

287 = 178 x 1 + 109

Step 3: We consider the new divisor 178 and the new remainder 109, and apply the division lemma to get

178 = 109 x 1 + 69

We consider the new divisor 109 and the new remainder 69,and apply the division lemma to get

109 = 69 x 1 + 40

We consider the new divisor 69 and the new remainder 40,and apply the division lemma to get

69 = 40 x 1 + 29

We consider the new divisor 40 and the new remainder 29,and apply the division lemma to get

40 = 29 x 1 + 11

We consider the new divisor 29 and the new remainder 11,and apply the division lemma to get

29 = 11 x 2 + 7

We consider the new divisor 11 and the new remainder 7,and apply the division lemma to get

11 = 7 x 1 + 4

We consider the new divisor 7 and the new remainder 4,and apply the division lemma to get

7 = 4 x 1 + 3

We consider the new divisor 4 and the new remainder 3,and apply the division lemma to get

4 = 3 x 1 + 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 752 and 287 is 1

Notice that 1 = HCF(3,1) = HCF(4,3) = HCF(7,4) = HCF(11,7) = HCF(29,11) = HCF(40,29) = HCF(69,40) = HCF(109,69) = HCF(178,109) = HCF(287,178) = HCF(752,287) .

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Frequently Asked Questions on HCF of 752, 287 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 752, 287?

Answer: HCF of 752, 287 is 1 the largest number that divides all the numbers leaving a remainder zero.

3. How to find HCF of 752, 287 using Euclid's Algorithm?

Answer: For arbitrary numbers 752, 287 apply Euclid’s Division Lemma in succession until you obtain a remainder zero. HCF is the remainder in the last but one step.