Highest Common Factor of 1904, 4535, 64142 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 1904, 4535, 64142 i.e. 1 the largest integer that leaves a remainder zero for all numbers.

HCF of 1904, 4535, 64142 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 1904, 4535, 64142 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 1904, 4535, 64142 is 1.

HCF(1904, 4535, 64142) = 1

HCF of 1904, 4535, 64142 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 1904, 4535, 64142 is 1.

Highest Common Factor of 1904,4535,64142 using Euclid's algorithm

Highest Common Factor of 1904,4535,64142 is 1

Step 1: Since 4535 > 1904, we apply the division lemma to 4535 and 1904, to get

4535 = 1904 x 2 + 727

Step 2: Since the reminder 1904 ≠ 0, we apply division lemma to 727 and 1904, to get

1904 = 727 x 2 + 450

Step 3: We consider the new divisor 727 and the new remainder 450, and apply the division lemma to get

727 = 450 x 1 + 277

We consider the new divisor 450 and the new remainder 277,and apply the division lemma to get

450 = 277 x 1 + 173

We consider the new divisor 277 and the new remainder 173,and apply the division lemma to get

277 = 173 x 1 + 104

We consider the new divisor 173 and the new remainder 104,and apply the division lemma to get

173 = 104 x 1 + 69

We consider the new divisor 104 and the new remainder 69,and apply the division lemma to get

104 = 69 x 1 + 35

We consider the new divisor 69 and the new remainder 35,and apply the division lemma to get

69 = 35 x 1 + 34

We consider the new divisor 35 and the new remainder 34,and apply the division lemma to get

35 = 34 x 1 + 1

We consider the new divisor 34 and the new remainder 1,and apply the division lemma to get

34 = 1 x 34 + 0

The remainder has now become zero, so our procedure stops. Since the divisor at this stage is 1, the HCF of 1904 and 4535 is 1

Notice that 1 = HCF(34,1) = HCF(35,34) = HCF(69,35) = HCF(104,69) = HCF(173,104) = HCF(277,173) = HCF(450,277) = HCF(727,450) = HCF(1904,727) = HCF(4535,1904) .

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

Step 1: Since 64142 > 1, we apply the division lemma to 64142 and 1, to get

64142 = 1 x 64142 + 0

The remainder has now become zero, so our procedure stops. Since the divisor at this stage is 1, the HCF of 1 and 64142 is 1

Notice that 1 = HCF(64142,1) .

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Frequently Asked Questions on HCF of 1904, 4535, 64142 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 1904, 4535, 64142?

Answer: HCF of 1904, 4535, 64142 is 1 the largest number that divides all the numbers leaving a remainder zero.

3. How to find HCF of 1904, 4535, 64142 using Euclid's Algorithm?

Answer: For arbitrary numbers 1904, 4535, 64142 apply Euclid’s Division Lemma in succession until you obtain a remainder zero. HCF is the remainder in the last but one step.