Highest Common Factor of 475, 743, 100 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 475, 743, 100 i.e. 1 the largest integer that leaves a remainder zero for all numbers.

HCF of 475, 743, 100 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 475, 743, 100 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 475, 743, 100 is 1.

HCF(475, 743, 100) = 1

HCF of 475, 743, 100 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 475, 743, 100 is 1.

Highest Common Factor of 475,743,100 using Euclid's algorithm

Highest Common Factor of 475,743,100 is 1

Step 1: Since 743 > 475, we apply the division lemma to 743 and 475, to get

743 = 475 x 1 + 268

Step 2: Since the reminder 475 ≠ 0, we apply division lemma to 268 and 475, to get

475 = 268 x 1 + 207

Step 3: We consider the new divisor 268 and the new remainder 207, and apply the division lemma to get

268 = 207 x 1 + 61

We consider the new divisor 207 and the new remainder 61,and apply the division lemma to get

207 = 61 x 3 + 24

We consider the new divisor 61 and the new remainder 24,and apply the division lemma to get

61 = 24 x 2 + 13

We consider the new divisor 24 and the new remainder 13,and apply the division lemma to get

24 = 13 x 1 + 11

We consider the new divisor 13 and the new remainder 11,and apply the division lemma to get

13 = 11 x 1 + 2

We consider the new divisor 11 and the new remainder 2,and apply the division lemma to get

11 = 2 x 5 + 1

We consider the new divisor 2 and the new remainder 1,and apply the division lemma 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 475 and 743 is 1

Notice that 1 = HCF(2,1) = HCF(11,2) = HCF(13,11) = HCF(24,13) = HCF(61,24) = HCF(207,61) = HCF(268,207) = HCF(475,268) = HCF(743,475) .

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

Step 1: Since 100 > 1, we apply the division lemma to 100 and 1, to get

100 = 1 x 100 + 0

The remainder has now become zero, so our procedure stops. Since the divisor at this stage is 1, the HCF of 1 and 100 is 1

Notice that 1 = HCF(100,1) .

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Frequently Asked Questions on HCF of 475, 743, 100 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 475, 743, 100?

Answer: HCF of 475, 743, 100 is 1 the largest number that divides all the numbers leaving a remainder zero.

3. How to find HCF of 475, 743, 100 using Euclid's Algorithm?

Answer: For arbitrary numbers 475, 743, 100 apply Euclid’s Division Lemma in succession until you obtain a remainder zero. HCF is the remainder in the last but one step.