Highest Common Factor of 7338, 7120, 53971 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 7338, 7120, 53971 i.e. 1 the largest integer that leaves a remainder zero for all numbers.

HCF of 7338, 7120, 53971 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 7338, 7120, 53971 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 7338, 7120, 53971 is 1.

HCF(7338, 7120, 53971) = 1

HCF of 7338, 7120, 53971 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 7338, 7120, 53971 is 1.

Highest Common Factor of 7338,7120,53971 using Euclid's algorithm

Highest Common Factor of 7338,7120,53971 is 1

Step 1: Since 7338 > 7120, we apply the division lemma to 7338 and 7120, to get

7338 = 7120 x 1 + 218

Step 2: Since the reminder 7120 ≠ 0, we apply division lemma to 218 and 7120, to get

7120 = 218 x 32 + 144

Step 3: We consider the new divisor 218 and the new remainder 144, and apply the division lemma to get

218 = 144 x 1 + 74

We consider the new divisor 144 and the new remainder 74,and apply the division lemma to get

144 = 74 x 1 + 70

We consider the new divisor 74 and the new remainder 70,and apply the division lemma to get

74 = 70 x 1 + 4

We consider the new divisor 70 and the new remainder 4,and apply the division lemma to get

70 = 4 x 17 + 2

We consider the new divisor 4 and the new remainder 2,and apply the division lemma to get

4 = 2 x 2 + 0

The remainder has now become zero, so our procedure stops. Since the divisor at this stage is 2, the HCF of 7338 and 7120 is 2

Notice that 2 = HCF(4,2) = HCF(70,4) = HCF(74,70) = HCF(144,74) = HCF(218,144) = HCF(7120,218) = HCF(7338,7120) .

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

Step 1: Since 53971 > 2, we apply the division lemma to 53971 and 2, to get

53971 = 2 x 26985 + 1

Step 2: Since the reminder 2 ≠ 0, we apply division lemma to 1 and 2, 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 2 and 53971 is 1

Notice that 1 = HCF(2,1) = HCF(53971,2) .

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Frequently Asked Questions on HCF of 7338, 7120, 53971 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 7338, 7120, 53971?

Answer: HCF of 7338, 7120, 53971 is 1 the largest number that divides all the numbers leaving a remainder zero.

3. How to find HCF of 7338, 7120, 53971 using Euclid's Algorithm?

Answer: For arbitrary numbers 7338, 7120, 53971 apply Euclid’s Division Lemma in succession until you obtain a remainder zero. HCF is the remainder in the last but one step.