Highest Common Factor of 7109, 1040, 88912 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 7109, 1040, 88912 i.e. 1 the largest integer that leaves a remainder zero for all numbers.

HCF of 7109, 1040, 88912 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 7109, 1040, 88912 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 7109, 1040, 88912 is 1.

HCF(7109, 1040, 88912) = 1

HCF of 7109, 1040, 88912 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 7109, 1040, 88912 is 1.

Highest Common Factor of 7109,1040,88912 using Euclid's algorithm

Highest Common Factor of 7109,1040,88912 is 1

Step 1: Since 7109 > 1040, we apply the division lemma to 7109 and 1040, to get

7109 = 1040 x 6 + 869

Step 2: Since the reminder 1040 ≠ 0, we apply division lemma to 869 and 1040, to get

1040 = 869 x 1 + 171

Step 3: We consider the new divisor 869 and the new remainder 171, and apply the division lemma to get

869 = 171 x 5 + 14

We consider the new divisor 171 and the new remainder 14,and apply the division lemma to get

171 = 14 x 12 + 3

We consider the new divisor 14 and the new remainder 3,and apply the division lemma to get

14 = 3 x 4 + 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 7109 and 1040 is 1

Notice that 1 = HCF(2,1) = HCF(3,2) = HCF(14,3) = HCF(171,14) = HCF(869,171) = HCF(1040,869) = HCF(7109,1040) .

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

Step 1: Since 88912 > 1, we apply the division lemma to 88912 and 1, to get

88912 = 1 x 88912 + 0

The remainder has now become zero, so our procedure stops. Since the divisor at this stage is 1, the HCF of 1 and 88912 is 1

Notice that 1 = HCF(88912,1) .

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Frequently Asked Questions on HCF of 7109, 1040, 88912 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 7109, 1040, 88912?

Answer: HCF of 7109, 1040, 88912 is 1 the largest number that divides all the numbers leaving a remainder zero.

3. How to find HCF of 7109, 1040, 88912 using Euclid's Algorithm?

Answer: For arbitrary numbers 7109, 1040, 88912 apply Euclid’s Division Lemma in succession until you obtain a remainder zero. HCF is the remainder in the last but one step.