Highest Common Factor of 103, 488, 149 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 103, 488, 149 i.e. 1 the largest integer that leaves a remainder zero for all numbers.

HCF of 103, 488, 149 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 103, 488, 149 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 103, 488, 149 is 1.

HCF(103, 488, 149) = 1

HCF of 103, 488, 149 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 103, 488, 149 is 1.

Highest Common Factor of 103,488,149 using Euclid's algorithm

Highest Common Factor of 103,488,149 is 1

Step 1: Since 488 > 103, we apply the division lemma to 488 and 103, to get

488 = 103 x 4 + 76

Step 2: Since the reminder 103 ≠ 0, we apply division lemma to 76 and 103, to get

103 = 76 x 1 + 27

Step 3: We consider the new divisor 76 and the new remainder 27, and apply the division lemma to get

76 = 27 x 2 + 22

We consider the new divisor 27 and the new remainder 22,and apply the division lemma to get

27 = 22 x 1 + 5

We consider the new divisor 22 and the new remainder 5,and apply the division lemma to get

22 = 5 x 4 + 2

We consider the new divisor 5 and the new remainder 2,and apply the division lemma to get

5 = 2 x 2 + 1

We consider the new divisor 2 and the new remainder 1,and apply the division lemma to get

2 = 1 x 2 + 0

The remainder has now become zero, so our procedure stops. Since the divisor at this stage is 1, the HCF of 103 and 488 is 1

Notice that 1 = HCF(2,1) = HCF(5,2) = HCF(22,5) = HCF(27,22) = HCF(76,27) = HCF(103,76) = HCF(488,103) .

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

Step 1: Since 149 > 1, we apply the division lemma to 149 and 1, to get

149 = 1 x 149 + 0

The remainder has now become zero, so our procedure stops. Since the divisor at this stage is 1, the HCF of 1 and 149 is 1

Notice that 1 = HCF(149,1) .

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Frequently Asked Questions on HCF of 103, 488, 149 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 103, 488, 149?

Answer: HCF of 103, 488, 149 is 1 the largest number that divides all the numbers leaving a remainder zero.

3. How to find HCF of 103, 488, 149 using Euclid's Algorithm?

Answer: For arbitrary numbers 103, 488, 149 apply Euclid’s Division Lemma in succession until you obtain a remainder zero. HCF is the remainder in the last but one step.