Highest Common Factor of 475, 658, 450 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, 658, 450 i.e. 1 the largest integer that leaves a remainder zero for all numbers.

HCF of 475, 658, 450 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, 658, 450 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, 658, 450 is 1.

HCF(475, 658, 450) = 1

HCF of 475, 658, 450 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, 658, 450 is 1.

Highest Common Factor of 475,658,450 using Euclid's algorithm

Highest Common Factor of 475,658,450 is 1

Step 1: Since 658 > 475, we apply the division lemma to 658 and 475, to get

658 = 475 x 1 + 183

Step 2: Since the reminder 475 ≠ 0, we apply division lemma to 183 and 475, to get

475 = 183 x 2 + 109

Step 3: We consider the new divisor 183 and the new remainder 109, and apply the division lemma to get

183 = 109 x 1 + 74

We consider the new divisor 109 and the new remainder 74,and apply the division lemma to get

109 = 74 x 1 + 35

We consider the new divisor 74 and the new remainder 35,and apply the division lemma to get

74 = 35 x 2 + 4

We consider the new divisor 35 and the new remainder 4,and apply the division lemma to get

35 = 4 x 8 + 3

We consider the new divisor 4 and the new remainder 3,and apply the division lemma to get

4 = 3 x 1 + 1

We consider the new divisor 3 and the new remainder 1,and apply the division lemma to get

3 = 1 x 3 + 0

The remainder has now become zero, so our procedure stops. Since the divisor at this stage is 1, the HCF of 475 and 658 is 1

Notice that 1 = HCF(3,1) = HCF(4,3) = HCF(35,4) = HCF(74,35) = HCF(109,74) = HCF(183,109) = HCF(475,183) = HCF(658,475) .

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

Step 1: Since 450 > 1, we apply the division lemma to 450 and 1, to get

450 = 1 x 450 + 0

The remainder has now become zero, so our procedure stops. Since the divisor at this stage is 1, the HCF of 1 and 450 is 1

Notice that 1 = HCF(450,1) .

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Frequently Asked Questions on HCF of 475, 658, 450 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, 658, 450?

Answer: HCF of 475, 658, 450 is 1 the largest number that divides all the numbers leaving a remainder zero.

3. How to find HCF of 475, 658, 450 using Euclid's Algorithm?

Answer: For arbitrary numbers 475, 658, 450 apply Euclid’s Division Lemma in succession until you obtain a remainder zero. HCF is the remainder in the last but one step.