Highest Common Factor of 654, 407, 513 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 654, 407, 513 i.e. 1 the largest integer that leaves a remainder zero for all numbers.

HCF of 654, 407, 513 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 654, 407, 513 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 654, 407, 513 is 1.

HCF(654, 407, 513) = 1

HCF of 654, 407, 513 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 654, 407, 513 is 1.

Highest Common Factor of 654,407,513 using Euclid's algorithm

Highest Common Factor of 654,407,513 is 1

Step 1: Since 654 > 407, we apply the division lemma to 654 and 407, to get

654 = 407 x 1 + 247

Step 2: Since the reminder 407 ≠ 0, we apply division lemma to 247 and 407, to get

407 = 247 x 1 + 160

Step 3: We consider the new divisor 247 and the new remainder 160, and apply the division lemma to get

247 = 160 x 1 + 87

We consider the new divisor 160 and the new remainder 87,and apply the division lemma to get

160 = 87 x 1 + 73

We consider the new divisor 87 and the new remainder 73,and apply the division lemma to get

87 = 73 x 1 + 14

We consider the new divisor 73 and the new remainder 14,and apply the division lemma to get

73 = 14 x 5 + 3

We consider the new divisor 14 and the new remainder 3,and apply the division lemma to get

14 = 3 x 4 + 2

We consider the new divisor 3 and the new remainder 2,and apply the division lemma to get

3 = 2 x 1 + 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 654 and 407 is 1

Notice that 1 = HCF(2,1) = HCF(3,2) = HCF(14,3) = HCF(73,14) = HCF(87,73) = HCF(160,87) = HCF(247,160) = HCF(407,247) = HCF(654,407) .

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

Step 1: Since 513 > 1, we apply the division lemma to 513 and 1, to get

513 = 1 x 513 + 0

The remainder has now become zero, so our procedure stops. Since the divisor at this stage is 1, the HCF of 1 and 513 is 1

Notice that 1 = HCF(513,1) .

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Frequently Asked Questions on HCF of 654, 407, 513 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 654, 407, 513?

Answer: HCF of 654, 407, 513 is 1 the largest number that divides all the numbers leaving a remainder zero.

3. How to find HCF of 654, 407, 513 using Euclid's Algorithm?

Answer: For arbitrary numbers 654, 407, 513 apply Euclid’s Division Lemma in succession until you obtain a remainder zero. HCF is the remainder in the last but one step.