Highest Common Factor of 6985, 7540, 22296 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 6985, 7540, 22296 i.e. 1 the largest integer that leaves a remainder zero for all numbers.

HCF of 6985, 7540, 22296 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 6985, 7540, 22296 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 6985, 7540, 22296 is 1.

HCF(6985, 7540, 22296) = 1

HCF of 6985, 7540, 22296 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 6985, 7540, 22296 is 1.

Highest Common Factor of 6985,7540,22296 using Euclid's algorithm

Highest Common Factor of 6985,7540,22296 is 1

Step 1: Since 7540 > 6985, we apply the division lemma to 7540 and 6985, to get

7540 = 6985 x 1 + 555

Step 2: Since the reminder 6985 ≠ 0, we apply division lemma to 555 and 6985, to get

6985 = 555 x 12 + 325

Step 3: We consider the new divisor 555 and the new remainder 325, and apply the division lemma to get

555 = 325 x 1 + 230

We consider the new divisor 325 and the new remainder 230,and apply the division lemma to get

325 = 230 x 1 + 95

We consider the new divisor 230 and the new remainder 95,and apply the division lemma to get

230 = 95 x 2 + 40

We consider the new divisor 95 and the new remainder 40,and apply the division lemma to get

95 = 40 x 2 + 15

We consider the new divisor 40 and the new remainder 15,and apply the division lemma to get

40 = 15 x 2 + 10

We consider the new divisor 15 and the new remainder 10,and apply the division lemma to get

15 = 10 x 1 + 5

We consider the new divisor 10 and the new remainder 5,and apply the division lemma to get

10 = 5 x 2 + 0

The remainder has now become zero, so our procedure stops. Since the divisor at this stage is 5, the HCF of 6985 and 7540 is 5

Notice that 5 = HCF(10,5) = HCF(15,10) = HCF(40,15) = HCF(95,40) = HCF(230,95) = HCF(325,230) = HCF(555,325) = HCF(6985,555) = HCF(7540,6985) .

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

Step 1: Since 22296 > 5, we apply the division lemma to 22296 and 5, to get

22296 = 5 x 4459 + 1

Step 2: Since the reminder 5 ≠ 0, we apply division lemma to 1 and 5, to get

5 = 1 x 5 + 0

The remainder has now become zero, so our procedure stops. Since the divisor at this stage is 1, the HCF of 5 and 22296 is 1

Notice that 1 = HCF(5,1) = HCF(22296,5) .

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Frequently Asked Questions on HCF of 6985, 7540, 22296 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 6985, 7540, 22296?

Answer: HCF of 6985, 7540, 22296 is 1 the largest number that divides all the numbers leaving a remainder zero.

3. How to find HCF of 6985, 7540, 22296 using Euclid's Algorithm?

Answer: For arbitrary numbers 6985, 7540, 22296 apply Euclid’s Division Lemma in succession until you obtain a remainder zero. HCF is the remainder in the last but one step.