Highest Common Factor of 164, 277, 281 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 164, 277, 281 i.e. 1 the largest integer that leaves a remainder zero for all numbers.

HCF of 164, 277, 281 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 164, 277, 281 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 164, 277, 281 is 1.

HCF(164, 277, 281) = 1

HCF of 164, 277, 281 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 164, 277, 281 is 1.

Highest Common Factor of 164,277,281 using Euclid's algorithm

Highest Common Factor of 164,277,281 is 1

Step 1: Since 277 > 164, we apply the division lemma to 277 and 164, to get

277 = 164 x 1 + 113

Step 2: Since the reminder 164 ≠ 0, we apply division lemma to 113 and 164, to get

164 = 113 x 1 + 51

Step 3: We consider the new divisor 113 and the new remainder 51, and apply the division lemma to get

113 = 51 x 2 + 11

We consider the new divisor 51 and the new remainder 11,and apply the division lemma to get

51 = 11 x 4 + 7

We consider the new divisor 11 and the new remainder 7,and apply the division lemma to get

11 = 7 x 1 + 4

We consider the new divisor 7 and the new remainder 4,and apply the division lemma to get

7 = 4 x 1 + 3

We consider the new divisor 4 and the new remainder 3,and apply the division lemma to get

4 = 3 x 1 + 1

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 164 and 277 is 1

Notice that 1 = HCF(3,1) = HCF(4,3) = HCF(7,4) = HCF(11,7) = HCF(51,11) = HCF(113,51) = HCF(164,113) = HCF(277,164) .

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

Step 1: Since 281 > 1, we apply the division lemma to 281 and 1, to get

281 = 1 x 281 + 0

The remainder has now become zero, so our procedure stops. Since the divisor at this stage is 1, the HCF of 1 and 281 is 1

Notice that 1 = HCF(281,1) .

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Frequently Asked Questions on HCF of 164, 277, 281 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 164, 277, 281?

Answer: HCF of 164, 277, 281 is 1 the largest number that divides all the numbers leaving a remainder zero.

3. How to find HCF of 164, 277, 281 using Euclid's Algorithm?

Answer: For arbitrary numbers 164, 277, 281 apply Euclid’s Division Lemma in succession until you obtain a remainder zero. HCF is the remainder in the last but one step.