Highest Common Factor of 1457, 8812 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 1457, 8812 i.e. 1 the largest integer that leaves a remainder zero for all numbers.

HCF of 1457, 8812 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 1457, 8812 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 1457, 8812 is 1.

HCF(1457, 8812) = 1

HCF of 1457, 8812 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 1457, 8812 is 1.

Highest Common Factor of 1457,8812 using Euclid's algorithm

Highest Common Factor of 1457,8812 is 1

Step 1: Since 8812 > 1457, we apply the division lemma to 8812 and 1457, to get

8812 = 1457 x 6 + 70

Step 2: Since the reminder 1457 ≠ 0, we apply division lemma to 70 and 1457, to get

1457 = 70 x 20 + 57

Step 3: We consider the new divisor 70 and the new remainder 57, and apply the division lemma to get

70 = 57 x 1 + 13

We consider the new divisor 57 and the new remainder 13,and apply the division lemma to get

57 = 13 x 4 + 5

We consider the new divisor 13 and the new remainder 5,and apply the division lemma to get

13 = 5 x 2 + 3

We consider the new divisor 5 and the new remainder 3,and apply the division lemma to get

5 = 3 x 1 + 2

We consider the new divisor 3 and the new remainder 2,and apply the division lemma to get

3 = 2 x 1 + 1

We consider the new divisor 2 and the new remainder 1,and apply the division lemma 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 1457 and 8812 is 1

Notice that 1 = HCF(2,1) = HCF(3,2) = HCF(5,3) = HCF(13,5) = HCF(57,13) = HCF(70,57) = HCF(1457,70) = HCF(8812,1457) .

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Frequently Asked Questions on HCF of 1457, 8812 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 1457, 8812?

Answer: HCF of 1457, 8812 is 1 the largest number that divides all the numbers leaving a remainder zero.

3. How to find HCF of 1457, 8812 using Euclid's Algorithm?

Answer: For arbitrary numbers 1457, 8812 apply Euclid’s Division Lemma in succession until you obtain a remainder zero. HCF is the remainder in the last but one step.