Highest Common Factor of 504, 836, 225 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 504, 836, 225 i.e. 1 the largest integer that leaves a remainder zero for all numbers.

HCF of 504, 836, 225 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 504, 836, 225 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 504, 836, 225 is 1.

HCF(504, 836, 225) = 1

HCF of 504, 836, 225 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 504, 836, 225 is 1.

Highest Common Factor of 504,836,225 using Euclid's algorithm

Highest Common Factor of 504,836,225 is 1

Step 1: Since 836 > 504, we apply the division lemma to 836 and 504, to get

836 = 504 x 1 + 332

Step 2: Since the reminder 504 ≠ 0, we apply division lemma to 332 and 504, to get

504 = 332 x 1 + 172

Step 3: We consider the new divisor 332 and the new remainder 172, and apply the division lemma to get

332 = 172 x 1 + 160

We consider the new divisor 172 and the new remainder 160,and apply the division lemma to get

172 = 160 x 1 + 12

We consider the new divisor 160 and the new remainder 12,and apply the division lemma to get

160 = 12 x 13 + 4

We consider the new divisor 12 and the new remainder 4,and apply the division lemma to get

12 = 4 x 3 + 0

The remainder has now become zero, so our procedure stops. Since the divisor at this stage is 4, the HCF of 504 and 836 is 4

Notice that 4 = HCF(12,4) = HCF(160,12) = HCF(172,160) = HCF(332,172) = HCF(504,332) = HCF(836,504) .

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

Step 1: Since 225 > 4, we apply the division lemma to 225 and 4, to get

225 = 4 x 56 + 1

Step 2: Since the reminder 4 ≠ 0, we apply division lemma to 1 and 4, 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 4 and 225 is 1

Notice that 1 = HCF(4,1) = HCF(225,4) .

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Frequently Asked Questions on HCF of 504, 836, 225 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 504, 836, 225?

Answer: HCF of 504, 836, 225 is 1 the largest number that divides all the numbers leaving a remainder zero.

3. How to find HCF of 504, 836, 225 using Euclid's Algorithm?

Answer: For arbitrary numbers 504, 836, 225 apply Euclid’s Division Lemma in succession until you obtain a remainder zero. HCF is the remainder in the last but one step.