Highest Common Factor of 4102, 6088, 57505 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 4102, 6088, 57505 i.e. 1 the largest integer that leaves a remainder zero for all numbers.

HCF of 4102, 6088, 57505 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 4102, 6088, 57505 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 4102, 6088, 57505 is 1.

HCF(4102, 6088, 57505) = 1

HCF of 4102, 6088, 57505 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 4102, 6088, 57505 is 1.

Highest Common Factor of 4102,6088,57505 using Euclid's algorithm

Highest Common Factor of 4102,6088,57505 is 1

Step 1: Since 6088 > 4102, we apply the division lemma to 6088 and 4102, to get

6088 = 4102 x 1 + 1986

Step 2: Since the reminder 4102 ≠ 0, we apply division lemma to 1986 and 4102, to get

4102 = 1986 x 2 + 130

Step 3: We consider the new divisor 1986 and the new remainder 130, and apply the division lemma to get

1986 = 130 x 15 + 36

We consider the new divisor 130 and the new remainder 36,and apply the division lemma to get

130 = 36 x 3 + 22

We consider the new divisor 36 and the new remainder 22,and apply the division lemma to get

36 = 22 x 1 + 14

We consider the new divisor 22 and the new remainder 14,and apply the division lemma to get

22 = 14 x 1 + 8

We consider the new divisor 14 and the new remainder 8,and apply the division lemma to get

14 = 8 x 1 + 6

We consider the new divisor 8 and the new remainder 6,and apply the division lemma to get

8 = 6 x 1 + 2

We consider the new divisor 6 and the new remainder 2,and apply the division lemma to get

6 = 2 x 3 + 0

The remainder has now become zero, so our procedure stops. Since the divisor at this stage is 2, the HCF of 4102 and 6088 is 2

Notice that 2 = HCF(6,2) = HCF(8,6) = HCF(14,8) = HCF(22,14) = HCF(36,22) = HCF(130,36) = HCF(1986,130) = HCF(4102,1986) = HCF(6088,4102) .

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

Step 1: Since 57505 > 2, we apply the division lemma to 57505 and 2, to get

57505 = 2 x 28752 + 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 57505 is 1

Notice that 1 = HCF(2,1) = HCF(57505,2) .

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Frequently Asked Questions on HCF of 4102, 6088, 57505 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 4102, 6088, 57505?

Answer: HCF of 4102, 6088, 57505 is 1 the largest number that divides all the numbers leaving a remainder zero.

3. How to find HCF of 4102, 6088, 57505 using Euclid's Algorithm?

Answer: For arbitrary numbers 4102, 6088, 57505 apply Euclid’s Division Lemma in succession until you obtain a remainder zero. HCF is the remainder in the last but one step.