Highest Common Factor of 712, 9042, 2251 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 712, 9042, 2251 i.e. 1 the largest integer that leaves a remainder zero for all numbers.

HCF of 712, 9042, 2251 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 712, 9042, 2251 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 712, 9042, 2251 is 1.

HCF(712, 9042, 2251) = 1

HCF of 712, 9042, 2251 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 712, 9042, 2251 is 1.

Highest Common Factor of 712,9042,2251 using Euclid's algorithm

Highest Common Factor of 712,9042,2251 is 1

Step 1: Since 9042 > 712, we apply the division lemma to 9042 and 712, to get

9042 = 712 x 12 + 498

Step 2: Since the reminder 712 ≠ 0, we apply division lemma to 498 and 712, to get

712 = 498 x 1 + 214

Step 3: We consider the new divisor 498 and the new remainder 214, and apply the division lemma to get

498 = 214 x 2 + 70

We consider the new divisor 214 and the new remainder 70,and apply the division lemma to get

214 = 70 x 3 + 4

We consider the new divisor 70 and the new remainder 4,and apply the division lemma to get

70 = 4 x 17 + 2

We consider the new divisor 4 and the new remainder 2,and apply the division lemma to get

4 = 2 x 2 + 0

The remainder has now become zero, so our procedure stops. Since the divisor at this stage is 2, the HCF of 712 and 9042 is 2

Notice that 2 = HCF(4,2) = HCF(70,4) = HCF(214,70) = HCF(498,214) = HCF(712,498) = HCF(9042,712) .

We can take hcf of as 1st numbers and next number as another number to apply in Euclidean lemma

Step 1: Since 2251 > 2, we apply the division lemma to 2251 and 2, to get

2251 = 2 x 1125 + 1

Step 2: Since the reminder 2 ≠ 0, we apply division lemma to 1 and 2, to get

2 = 1 x 2 + 0

The remainder has now become zero, so our procedure stops. Since the divisor at this stage is 1, the HCF of 2 and 2251 is 1

Notice that 1 = HCF(2,1) = HCF(2251,2) .

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Frequently Asked Questions on HCF of 712, 9042, 2251 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 712, 9042, 2251?

Answer: HCF of 712, 9042, 2251 is 1 the largest number that divides all the numbers leaving a remainder zero.

3. How to find HCF of 712, 9042, 2251 using Euclid's Algorithm?

Answer: For arbitrary numbers 712, 9042, 2251 apply Euclid’s Division Lemma in succession until you obtain a remainder zero. HCF is the remainder in the last but one step.