Highest Common Factor of 8922, 8309, 70344 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 8922, 8309, 70344 i.e. 1 the largest integer that leaves a remainder zero for all numbers.

HCF of 8922, 8309, 70344 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 8922, 8309, 70344 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 8922, 8309, 70344 is 1.

HCF(8922, 8309, 70344) = 1

HCF of 8922, 8309, 70344 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 8922, 8309, 70344 is 1.

Highest Common Factor of 8922,8309,70344 using Euclid's algorithm

Highest Common Factor of 8922,8309,70344 is 1

Step 1: Since 8922 > 8309, we apply the division lemma to 8922 and 8309, to get

8922 = 8309 x 1 + 613

Step 2: Since the reminder 8309 ≠ 0, we apply division lemma to 613 and 8309, to get

8309 = 613 x 13 + 340

Step 3: We consider the new divisor 613 and the new remainder 340, and apply the division lemma to get

613 = 340 x 1 + 273

We consider the new divisor 340 and the new remainder 273,and apply the division lemma to get

340 = 273 x 1 + 67

We consider the new divisor 273 and the new remainder 67,and apply the division lemma to get

273 = 67 x 4 + 5

We consider the new divisor 67 and the new remainder 5,and apply the division lemma to get

67 = 5 x 13 + 2

We consider the new divisor 5 and the new remainder 2,and apply the division lemma to get

5 = 2 x 2 + 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 8922 and 8309 is 1

Notice that 1 = HCF(2,1) = HCF(5,2) = HCF(67,5) = HCF(273,67) = HCF(340,273) = HCF(613,340) = HCF(8309,613) = HCF(8922,8309) .

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

Step 1: Since 70344 > 1, we apply the division lemma to 70344 and 1, to get

70344 = 1 x 70344 + 0

The remainder has now become zero, so our procedure stops. Since the divisor at this stage is 1, the HCF of 1 and 70344 is 1

Notice that 1 = HCF(70344,1) .

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Frequently Asked Questions on HCF of 8922, 8309, 70344 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 8922, 8309, 70344?

Answer: HCF of 8922, 8309, 70344 is 1 the largest number that divides all the numbers leaving a remainder zero.

3. How to find HCF of 8922, 8309, 70344 using Euclid's Algorithm?

Answer: For arbitrary numbers 8922, 8309, 70344 apply Euclid’s Division Lemma in succession until you obtain a remainder zero. HCF is the remainder in the last but one step.