Highest Common Factor of 675, 504, 428 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 675, 504, 428 i.e. 1 the largest integer that leaves a remainder zero for all numbers.

HCF of 675, 504, 428 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 675, 504, 428 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 675, 504, 428 is 1.

HCF(675, 504, 428) = 1

HCF of 675, 504, 428 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 675, 504, 428 is 1.

Highest Common Factor of 675,504,428 using Euclid's algorithm

Highest Common Factor of 675,504,428 is 1

Step 1: Since 675 > 504, we apply the division lemma to 675 and 504, to get

675 = 504 x 1 + 171

Step 2: Since the reminder 504 ≠ 0, we apply division lemma to 171 and 504, to get

504 = 171 x 2 + 162

Step 3: We consider the new divisor 171 and the new remainder 162, and apply the division lemma to get

171 = 162 x 1 + 9

We consider the new divisor 162 and the new remainder 9, and apply the division lemma to get

162 = 9 x 18 + 0

The remainder has now become zero, so our procedure stops. Since the divisor at this stage is 9, the HCF of 675 and 504 is 9

Notice that 9 = HCF(162,9) = HCF(171,162) = HCF(504,171) = HCF(675,504) .

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

Step 1: Since 428 > 9, we apply the division lemma to 428 and 9, to get

428 = 9 x 47 + 5

Step 2: Since the reminder 9 ≠ 0, we apply division lemma to 5 and 9, to get

9 = 5 x 1 + 4

Step 3: We consider the new divisor 5 and the new remainder 4, and apply the division lemma to get

5 = 4 x 1 + 1

We consider the new divisor 4 and the new remainder 1, and apply the division lemma to get

4 = 1 x 4 + 0

The remainder has now become zero, so our procedure stops. Since the divisor at this stage is 1, the HCF of 9 and 428 is 1

Notice that 1 = HCF(4,1) = HCF(5,4) = HCF(9,5) = HCF(428,9) .

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Frequently Asked Questions on HCF of 675, 504, 428 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 675, 504, 428?

Answer: HCF of 675, 504, 428 is 1 the largest number that divides all the numbers leaving a remainder zero.

3. How to find HCF of 675, 504, 428 using Euclid's Algorithm?

Answer: For arbitrary numbers 675, 504, 428 apply Euclid’s Division Lemma in succession until you obtain a remainder zero. HCF is the remainder in the last but one step.