Highest Common Factor of 6040, 7980, 71167 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 6040, 7980, 71167 i.e. 1 the largest integer that leaves a remainder zero for all numbers.

HCF of 6040, 7980, 71167 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 6040, 7980, 71167 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 6040, 7980, 71167 is 1.

HCF(6040, 7980, 71167) = 1

HCF of 6040, 7980, 71167 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 6040, 7980, 71167 is 1.

Highest Common Factor of 6040,7980,71167 using Euclid's algorithm

Highest Common Factor of 6040,7980,71167 is 1

Step 1: Since 7980 > 6040, we apply the division lemma to 7980 and 6040, to get

7980 = 6040 x 1 + 1940

Step 2: Since the reminder 6040 ≠ 0, we apply division lemma to 1940 and 6040, to get

6040 = 1940 x 3 + 220

Step 3: We consider the new divisor 1940 and the new remainder 220, and apply the division lemma to get

1940 = 220 x 8 + 180

We consider the new divisor 220 and the new remainder 180,and apply the division lemma to get

220 = 180 x 1 + 40

We consider the new divisor 180 and the new remainder 40,and apply the division lemma to get

180 = 40 x 4 + 20

We consider the new divisor 40 and the new remainder 20,and apply the division lemma to get

40 = 20 x 2 + 0

The remainder has now become zero, so our procedure stops. Since the divisor at this stage is 20, the HCF of 6040 and 7980 is 20

Notice that 20 = HCF(40,20) = HCF(180,40) = HCF(220,180) = HCF(1940,220) = HCF(6040,1940) = HCF(7980,6040) .

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

Step 1: Since 71167 > 20, we apply the division lemma to 71167 and 20, to get

71167 = 20 x 3558 + 7

Step 2: Since the reminder 20 ≠ 0, we apply division lemma to 7 and 20, to get

20 = 7 x 2 + 6

Step 3: We consider the new divisor 7 and the new remainder 6, and apply the division lemma to get

7 = 6 x 1 + 1

We consider the new divisor 6 and the new remainder 1, and apply the division lemma to get

6 = 1 x 6 + 0

The remainder has now become zero, so our procedure stops. Since the divisor at this stage is 1, the HCF of 20 and 71167 is 1

Notice that 1 = HCF(6,1) = HCF(7,6) = HCF(20,7) = HCF(71167,20) .

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Frequently Asked Questions on HCF of 6040, 7980, 71167 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 6040, 7980, 71167?

Answer: HCF of 6040, 7980, 71167 is 1 the largest number that divides all the numbers leaving a remainder zero.

3. How to find HCF of 6040, 7980, 71167 using Euclid's Algorithm?

Answer: For arbitrary numbers 6040, 7980, 71167 apply Euclid’s Division Lemma in succession until you obtain a remainder zero. HCF is the remainder in the last but one step.