Highest Common Factor of 6837, 7222, 89040 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 6837, 7222, 89040 i.e. 1 the largest integer that leaves a remainder zero for all numbers.

HCF of 6837, 7222, 89040 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 6837, 7222, 89040 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 6837, 7222, 89040 is 1.

HCF(6837, 7222, 89040) = 1

HCF of 6837, 7222, 89040 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 6837, 7222, 89040 is 1.

Highest Common Factor of 6837,7222,89040 using Euclid's algorithm

Highest Common Factor of 6837,7222,89040 is 1

Step 1: Since 7222 > 6837, we apply the division lemma to 7222 and 6837, to get

7222 = 6837 x 1 + 385

Step 2: Since the reminder 6837 ≠ 0, we apply division lemma to 385 and 6837, to get

6837 = 385 x 17 + 292

Step 3: We consider the new divisor 385 and the new remainder 292, and apply the division lemma to get

385 = 292 x 1 + 93

We consider the new divisor 292 and the new remainder 93,and apply the division lemma to get

292 = 93 x 3 + 13

We consider the new divisor 93 and the new remainder 13,and apply the division lemma to get

93 = 13 x 7 + 2

We consider the new divisor 13 and the new remainder 2,and apply the division lemma to get

13 = 2 x 6 + 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 6837 and 7222 is 1

Notice that 1 = HCF(2,1) = HCF(13,2) = HCF(93,13) = HCF(292,93) = HCF(385,292) = HCF(6837,385) = HCF(7222,6837) .

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

Step 1: Since 89040 > 1, we apply the division lemma to 89040 and 1, to get

89040 = 1 x 89040 + 0

The remainder has now become zero, so our procedure stops. Since the divisor at this stage is 1, the HCF of 1 and 89040 is 1

Notice that 1 = HCF(89040,1) .

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Frequently Asked Questions on HCF of 6837, 7222, 89040 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 6837, 7222, 89040?

Answer: HCF of 6837, 7222, 89040 is 1 the largest number that divides all the numbers leaving a remainder zero.

3. How to find HCF of 6837, 7222, 89040 using Euclid's Algorithm?

Answer: For arbitrary numbers 6837, 7222, 89040 apply Euclid’s Division Lemma in succession until you obtain a remainder zero. HCF is the remainder in the last but one step.