Highest Common Factor of 438, 696, 254 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 438, 696, 254 i.e. 2 the largest integer that leaves a remainder zero for all numbers.

HCF of 438, 696, 254 is 2 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 438, 696, 254 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 438, 696, 254 is 2.

HCF(438, 696, 254) = 2

HCF of 438, 696, 254 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 438, 696, 254 is 2.

Highest Common Factor of 438,696,254 using Euclid's algorithm

Highest Common Factor of 438,696,254 is 2

Step 1: Since 696 > 438, we apply the division lemma to 696 and 438, to get

696 = 438 x 1 + 258

Step 2: Since the reminder 438 ≠ 0, we apply division lemma to 258 and 438, to get

438 = 258 x 1 + 180

Step 3: We consider the new divisor 258 and the new remainder 180, and apply the division lemma to get

258 = 180 x 1 + 78

We consider the new divisor 180 and the new remainder 78,and apply the division lemma to get

180 = 78 x 2 + 24

We consider the new divisor 78 and the new remainder 24,and apply the division lemma to get

78 = 24 x 3 + 6

We consider the new divisor 24 and the new remainder 6,and apply the division lemma to get

24 = 6 x 4 + 0

The remainder has now become zero, so our procedure stops. Since the divisor at this stage is 6, the HCF of 438 and 696 is 6

Notice that 6 = HCF(24,6) = HCF(78,24) = HCF(180,78) = HCF(258,180) = HCF(438,258) = HCF(696,438) .

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

Step 1: Since 254 > 6, we apply the division lemma to 254 and 6, to get

254 = 6 x 42 + 2

Step 2: Since the reminder 6 ≠ 0, we apply division lemma to 2 and 6, to get

6 = 2 x 3 + 0

The remainder has now become zero, so our procedure stops. Since the divisor at this stage is 2, the HCF of 6 and 254 is 2

Notice that 2 = HCF(6,2) = HCF(254,6) .

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Frequently Asked Questions on HCF of 438, 696, 254 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 438, 696, 254?

Answer: HCF of 438, 696, 254 is 2 the largest number that divides all the numbers leaving a remainder zero.

3. How to find HCF of 438, 696, 254 using Euclid's Algorithm?

Answer: For arbitrary numbers 438, 696, 254 apply Euclid’s Division Lemma in succession until you obtain a remainder zero. HCF is the remainder in the last but one step.