Highest Common Factor of 4660, 5888, 19872 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 4660, 5888, 19872 i.e. 4 the largest integer that leaves a remainder zero for all numbers.

HCF of 4660, 5888, 19872 is 4 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 4660, 5888, 19872 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 4660, 5888, 19872 is 4.

HCF(4660, 5888, 19872) = 4

HCF of 4660, 5888, 19872 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 4660, 5888, 19872 is 4.

Highest Common Factor of 4660,5888,19872 using Euclid's algorithm

Highest Common Factor of 4660,5888,19872 is 4

Step 1: Since 5888 > 4660, we apply the division lemma to 5888 and 4660, to get

5888 = 4660 x 1 + 1228

Step 2: Since the reminder 4660 ≠ 0, we apply division lemma to 1228 and 4660, to get

4660 = 1228 x 3 + 976

Step 3: We consider the new divisor 1228 and the new remainder 976, and apply the division lemma to get

1228 = 976 x 1 + 252

We consider the new divisor 976 and the new remainder 252,and apply the division lemma to get

976 = 252 x 3 + 220

We consider the new divisor 252 and the new remainder 220,and apply the division lemma to get

252 = 220 x 1 + 32

We consider the new divisor 220 and the new remainder 32,and apply the division lemma to get

220 = 32 x 6 + 28

We consider the new divisor 32 and the new remainder 28,and apply the division lemma to get

32 = 28 x 1 + 4

We consider the new divisor 28 and the new remainder 4,and apply the division lemma to get

28 = 4 x 7 + 0

The remainder has now become zero, so our procedure stops. Since the divisor at this stage is 4, the HCF of 4660 and 5888 is 4

Notice that 4 = HCF(28,4) = HCF(32,28) = HCF(220,32) = HCF(252,220) = HCF(976,252) = HCF(1228,976) = HCF(4660,1228) = HCF(5888,4660) .

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

Step 1: Since 19872 > 4, we apply the division lemma to 19872 and 4, to get

19872 = 4 x 4968 + 0

The remainder has now become zero, so our procedure stops. Since the divisor at this stage is 4, the HCF of 4 and 19872 is 4

Notice that 4 = HCF(19872,4) .

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Frequently Asked Questions on HCF of 4660, 5888, 19872 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 4660, 5888, 19872?

Answer: HCF of 4660, 5888, 19872 is 4 the largest number that divides all the numbers leaving a remainder zero.

3. How to find HCF of 4660, 5888, 19872 using Euclid's Algorithm?

Answer: For arbitrary numbers 4660, 5888, 19872 apply Euclid’s Division Lemma in succession until you obtain a remainder zero. HCF is the remainder in the last but one step.