Highest Common Factor of 488, 862, 475 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 488, 862, 475 i.e. 1 the largest integer that leaves a remainder zero for all numbers.

HCF of 488, 862, 475 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 488, 862, 475 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 488, 862, 475 is 1.

HCF(488, 862, 475) = 1

HCF of 488, 862, 475 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 488, 862, 475 is 1.

Highest Common Factor of 488,862,475 using Euclid's algorithm

Highest Common Factor of 488,862,475 is 1

Step 1: Since 862 > 488, we apply the division lemma to 862 and 488, to get

862 = 488 x 1 + 374

Step 2: Since the reminder 488 ≠ 0, we apply division lemma to 374 and 488, to get

488 = 374 x 1 + 114

Step 3: We consider the new divisor 374 and the new remainder 114, and apply the division lemma to get

374 = 114 x 3 + 32

We consider the new divisor 114 and the new remainder 32,and apply the division lemma to get

114 = 32 x 3 + 18

We consider the new divisor 32 and the new remainder 18,and apply the division lemma to get

32 = 18 x 1 + 14

We consider the new divisor 18 and the new remainder 14,and apply the division lemma to get

18 = 14 x 1 + 4

We consider the new divisor 14 and the new remainder 4,and apply the division lemma to get

14 = 4 x 3 + 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 488 and 862 is 2

Notice that 2 = HCF(4,2) = HCF(14,4) = HCF(18,14) = HCF(32,18) = HCF(114,32) = HCF(374,114) = HCF(488,374) = HCF(862,488) .

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

Step 1: Since 475 > 2, we apply the division lemma to 475 and 2, to get

475 = 2 x 237 + 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 475 is 1

Notice that 1 = HCF(2,1) = HCF(475,2) .

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Frequently Asked Questions on HCF of 488, 862, 475 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 488, 862, 475?

Answer: HCF of 488, 862, 475 is 1 the largest number that divides all the numbers leaving a remainder zero.

3. How to find HCF of 488, 862, 475 using Euclid's Algorithm?

Answer: For arbitrary numbers 488, 862, 475 apply Euclid’s Division Lemma in succession until you obtain a remainder zero. HCF is the remainder in the last but one step.