Highest Common Factor of 456, 251, 198, 165 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 456, 251, 198, 165 i.e. 1 the largest integer that leaves a remainder zero for all numbers.

HCF of 456, 251, 198, 165 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 456, 251, 198, 165 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 456, 251, 198, 165 is 1.

HCF(456, 251, 198, 165) = 1

HCF of 456, 251, 198, 165 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 456, 251, 198, 165 is 1.

Highest Common Factor of 456,251,198,165 using Euclid's algorithm

Highest Common Factor of 456,251,198,165 is 1

Step 1: Since 456 > 251, we apply the division lemma to 456 and 251, to get

456 = 251 x 1 + 205

Step 2: Since the reminder 251 ≠ 0, we apply division lemma to 205 and 251, to get

251 = 205 x 1 + 46

Step 3: We consider the new divisor 205 and the new remainder 46, and apply the division lemma to get

205 = 46 x 4 + 21

We consider the new divisor 46 and the new remainder 21,and apply the division lemma to get

46 = 21 x 2 + 4

We consider the new divisor 21 and the new remainder 4,and apply the division lemma to get

21 = 4 x 5 + 1

We consider the new divisor 4 and the new remainder 1,and apply the division lemma to get

4 = 1 x 4 + 0

The remainder has now become zero, so our procedure stops. Since the divisor at this stage is 1, the HCF of 456 and 251 is 1

Notice that 1 = HCF(4,1) = HCF(21,4) = HCF(46,21) = HCF(205,46) = HCF(251,205) = HCF(456,251) .

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

Step 1: Since 198 > 1, we apply the division lemma to 198 and 1, to get

198 = 1 x 198 + 0

The remainder has now become zero, so our procedure stops. Since the divisor at this stage is 1, the HCF of 1 and 198 is 1

Notice that 1 = HCF(198,1) .

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

Step 1: Since 165 > 1, we apply the division lemma to 165 and 1, to get

165 = 1 x 165 + 0

The remainder has now become zero, so our procedure stops. Since the divisor at this stage is 1, the HCF of 1 and 165 is 1

Notice that 1 = HCF(165,1) .

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Frequently Asked Questions on HCF of 456, 251, 198, 165 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 456, 251, 198, 165?

Answer: HCF of 456, 251, 198, 165 is 1 the largest number that divides all the numbers leaving a remainder zero.

3. How to find HCF of 456, 251, 198, 165 using Euclid's Algorithm?

Answer: For arbitrary numbers 456, 251, 198, 165 apply Euclid’s Division Lemma in succession until you obtain a remainder zero. HCF is the remainder in the last but one step.