Highest Common Factor of 4135, 3574 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 4135, 3574 i.e. 1 the largest integer that leaves a remainder zero for all numbers.

HCF of 4135, 3574 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 4135, 3574 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 4135, 3574 is 1.

HCF(4135, 3574) = 1

HCF of 4135, 3574 using Euclid's algorithm

Highest common factor or Highest common divisor (hcd) can be calculated by Euclid's algotithm.

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Highest common factor (HCF) of 4135, 3574 is 1.

Highest Common Factor of 4135,3574 using Euclid's algorithm

Highest Common Factor of 4135,3574 is 1

Step 1: Since 4135 > 3574, we apply the division lemma to 4135 and 3574, to get

4135 = 3574 x 1 + 561

Step 2: Since the reminder 3574 ≠ 0, we apply division lemma to 561 and 3574, to get

3574 = 561 x 6 + 208

Step 3: We consider the new divisor 561 and the new remainder 208, and apply the division lemma to get

561 = 208 x 2 + 145

We consider the new divisor 208 and the new remainder 145,and apply the division lemma to get

208 = 145 x 1 + 63

We consider the new divisor 145 and the new remainder 63,and apply the division lemma to get

145 = 63 x 2 + 19

We consider the new divisor 63 and the new remainder 19,and apply the division lemma to get

63 = 19 x 3 + 6

We consider the new divisor 19 and the new remainder 6,and apply the division lemma to get

19 = 6 x 3 + 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 4135 and 3574 is 1

Notice that 1 = HCF(6,1) = HCF(19,6) = HCF(63,19) = HCF(145,63) = HCF(208,145) = HCF(561,208) = HCF(3574,561) = HCF(4135,3574) .

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Frequently Asked Questions on HCF of 4135, 3574 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 4135, 3574?

Answer: HCF of 4135, 3574 is 1 the largest number that divides all the numbers leaving a remainder zero.

3. How to find HCF of 4135, 3574 using Euclid's Algorithm?

Answer: For arbitrary numbers 4135, 3574 apply Euclid’s Division Lemma in succession until you obtain a remainder zero. HCF is the remainder in the last but one step.