Highest Common Factor of 432, 252, 354 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 432, 252, 354 i.e. 6 the largest integer that leaves a remainder zero for all numbers.

HCF of 432, 252, 354 is 6 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 432, 252, 354 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 432, 252, 354 is 6.

HCF(432, 252, 354) = 6

HCF of 432, 252, 354 using Euclid's algorithm

Highest common factor or Highest common divisor (hcd) can be calculated by Euclid's algotithm.

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Highest common factor (HCF) of 432, 252, 354 is 6.

Highest Common Factor of 432,252,354 using Euclid's algorithm

Highest Common Factor of 432,252,354 is 6

Step 1: Since 432 > 252, we apply the division lemma to 432 and 252, to get

432 = 252 x 1 + 180

Step 2: Since the reminder 252 ≠ 0, we apply division lemma to 180 and 252, to get

252 = 180 x 1 + 72

Step 3: We consider the new divisor 180 and the new remainder 72, and apply the division lemma to get

180 = 72 x 2 + 36

We consider the new divisor 72 and the new remainder 36, and apply the division lemma to get

72 = 36 x 2 + 0

The remainder has now become zero, so our procedure stops. Since the divisor at this stage is 36, the HCF of 432 and 252 is 36

Notice that 36 = HCF(72,36) = HCF(180,72) = HCF(252,180) = HCF(432,252) .

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

Step 1: Since 354 > 36, we apply the division lemma to 354 and 36, to get

354 = 36 x 9 + 30

Step 2: Since the reminder 36 ≠ 0, we apply division lemma to 30 and 36, to get

36 = 30 x 1 + 6

Step 3: We consider the new divisor 30 and the new remainder 6, and apply the division lemma to get

30 = 6 x 5 + 0

The remainder has now become zero, so our procedure stops. Since the divisor at this stage is 6, the HCF of 36 and 354 is 6

Notice that 6 = HCF(30,6) = HCF(36,30) = HCF(354,36) .

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Frequently Asked Questions on HCF of 432, 252, 354 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 432, 252, 354?

Answer: HCF of 432, 252, 354 is 6 the largest number that divides all the numbers leaving a remainder zero.

3. How to find HCF of 432, 252, 354 using Euclid's Algorithm?

Answer: For arbitrary numbers 432, 252, 354 apply Euclid’s Division Lemma in succession until you obtain a remainder zero. HCF is the remainder in the last but one step.