Highest Common Factor of 451, 735, 176 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 451, 735, 176 i.e. 1 the largest integer that leaves a remainder zero for all numbers.

HCF of 451, 735, 176 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 451, 735, 176 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 451, 735, 176 is 1.

HCF(451, 735, 176) = 1

HCF of 451, 735, 176 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 451, 735, 176 is 1.

Highest Common Factor of 451,735,176 using Euclid's algorithm

Highest Common Factor of 451,735,176 is 1

Step 1: Since 735 > 451, we apply the division lemma to 735 and 451, to get

735 = 451 x 1 + 284

Step 2: Since the reminder 451 ≠ 0, we apply division lemma to 284 and 451, to get

451 = 284 x 1 + 167

Step 3: We consider the new divisor 284 and the new remainder 167, and apply the division lemma to get

284 = 167 x 1 + 117

We consider the new divisor 167 and the new remainder 117,and apply the division lemma to get

167 = 117 x 1 + 50

We consider the new divisor 117 and the new remainder 50,and apply the division lemma to get

117 = 50 x 2 + 17

We consider the new divisor 50 and the new remainder 17,and apply the division lemma to get

50 = 17 x 2 + 16

We consider the new divisor 17 and the new remainder 16,and apply the division lemma to get

17 = 16 x 1 + 1

We consider the new divisor 16 and the new remainder 1,and apply the division lemma to get

16 = 1 x 16 + 0

The remainder has now become zero, so our procedure stops. Since the divisor at this stage is 1, the HCF of 451 and 735 is 1

Notice that 1 = HCF(16,1) = HCF(17,16) = HCF(50,17) = HCF(117,50) = HCF(167,117) = HCF(284,167) = HCF(451,284) = HCF(735,451) .

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

Step 1: Since 176 > 1, we apply the division lemma to 176 and 1, to get

176 = 1 x 176 + 0

The remainder has now become zero, so our procedure stops. Since the divisor at this stage is 1, the HCF of 1 and 176 is 1

Notice that 1 = HCF(176,1) .

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Frequently Asked Questions on HCF of 451, 735, 176 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 451, 735, 176?

Answer: HCF of 451, 735, 176 is 1 the largest number that divides all the numbers leaving a remainder zero.

3. How to find HCF of 451, 735, 176 using Euclid's Algorithm?

Answer: For arbitrary numbers 451, 735, 176 apply Euclid’s Division Lemma in succession until you obtain a remainder zero. HCF is the remainder in the last but one step.