Highest Common Factor of 248, 388, 135 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 248, 388, 135 i.e. 1 the largest integer that leaves a remainder zero for all numbers.

HCF of 248, 388, 135 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 248, 388, 135 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 248, 388, 135 is 1.

HCF(248, 388, 135) = 1

HCF of 248, 388, 135 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 248, 388, 135 is 1.

Highest Common Factor of 248,388,135 using Euclid's algorithm

Highest Common Factor of 248,388,135 is 1

Step 1: Since 388 > 248, we apply the division lemma to 388 and 248, to get

388 = 248 x 1 + 140

Step 2: Since the reminder 248 ≠ 0, we apply division lemma to 140 and 248, to get

248 = 140 x 1 + 108

Step 3: We consider the new divisor 140 and the new remainder 108, and apply the division lemma to get

140 = 108 x 1 + 32

We consider the new divisor 108 and the new remainder 32,and apply the division lemma to get

108 = 32 x 3 + 12

We consider the new divisor 32 and the new remainder 12,and apply the division lemma to get

32 = 12 x 2 + 8

We consider the new divisor 12 and the new remainder 8,and apply the division lemma to get

12 = 8 x 1 + 4

We consider the new divisor 8 and the new remainder 4,and apply the division lemma to get

8 = 4 x 2 + 0

The remainder has now become zero, so our procedure stops. Since the divisor at this stage is 4, the HCF of 248 and 388 is 4

Notice that 4 = HCF(8,4) = HCF(12,8) = HCF(32,12) = HCF(108,32) = HCF(140,108) = HCF(248,140) = HCF(388,248) .

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

Step 1: Since 135 > 4, we apply the division lemma to 135 and 4, to get

135 = 4 x 33 + 3

Step 2: Since the reminder 4 ≠ 0, we apply division lemma to 3 and 4, to get

4 = 3 x 1 + 1

Step 3: 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 4 and 135 is 1

Notice that 1 = HCF(3,1) = HCF(4,3) = HCF(135,4) .

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Frequently Asked Questions on HCF of 248, 388, 135 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 248, 388, 135?

Answer: HCF of 248, 388, 135 is 1 the largest number that divides all the numbers leaving a remainder zero.

3. How to find HCF of 248, 388, 135 using Euclid's Algorithm?

Answer: For arbitrary numbers 248, 388, 135 apply Euclid’s Division Lemma in succession until you obtain a remainder zero. HCF is the remainder in the last but one step.