Highest Common Factor of 148, 262, 205 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 148, 262, 205 i.e. 1 the largest integer that leaves a remainder zero for all numbers.

HCF of 148, 262, 205 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 148, 262, 205 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 148, 262, 205 is 1.

HCF(148, 262, 205) = 1

HCF of 148, 262, 205 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 148, 262, 205 is 1.

Highest Common Factor of 148,262,205 using Euclid's algorithm

Highest Common Factor of 148,262,205 is 1

Step 1: Since 262 > 148, we apply the division lemma to 262 and 148, to get

262 = 148 x 1 + 114

Step 2: Since the reminder 148 ≠ 0, we apply division lemma to 114 and 148, to get

148 = 114 x 1 + 34

Step 3: We consider the new divisor 114 and the new remainder 34, and apply the division lemma to get

114 = 34 x 3 + 12

We consider the new divisor 34 and the new remainder 12,and apply the division lemma to get

34 = 12 x 2 + 10

We consider the new divisor 12 and the new remainder 10,and apply the division lemma to get

12 = 10 x 1 + 2

We consider the new divisor 10 and the new remainder 2,and apply the division lemma to get

10 = 2 x 5 + 0

The remainder has now become zero, so our procedure stops. Since the divisor at this stage is 2, the HCF of 148 and 262 is 2

Notice that 2 = HCF(10,2) = HCF(12,10) = HCF(34,12) = HCF(114,34) = HCF(148,114) = HCF(262,148) .

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

Step 1: Since 205 > 2, we apply the division lemma to 205 and 2, to get

205 = 2 x 102 + 1

Step 2: Since the reminder 2 ≠ 0, we apply division lemma to 1 and 2, 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 2 and 205 is 1

Notice that 1 = HCF(2,1) = HCF(205,2) .

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Frequently Asked Questions on HCF of 148, 262, 205 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 148, 262, 205?

Answer: HCF of 148, 262, 205 is 1 the largest number that divides all the numbers leaving a remainder zero.

3. How to find HCF of 148, 262, 205 using Euclid's Algorithm?

Answer: For arbitrary numbers 148, 262, 205 apply Euclid’s Division Lemma in succession until you obtain a remainder zero. HCF is the remainder in the last but one step.