Highest Common Factor of 207, 578, 459 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 207, 578, 459 i.e. 1 the largest integer that leaves a remainder zero for all numbers.

HCF of 207, 578, 459 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 207, 578, 459 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 207, 578, 459 is 1.

HCF(207, 578, 459) = 1

HCF of 207, 578, 459 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 207, 578, 459 is 1.

Highest Common Factor of 207,578,459 using Euclid's algorithm

Highest Common Factor of 207,578,459 is 1

Step 1: Since 578 > 207, we apply the division lemma to 578 and 207, to get

578 = 207 x 2 + 164

Step 2: Since the reminder 207 ≠ 0, we apply division lemma to 164 and 207, to get

207 = 164 x 1 + 43

Step 3: We consider the new divisor 164 and the new remainder 43, and apply the division lemma to get

164 = 43 x 3 + 35

We consider the new divisor 43 and the new remainder 35,and apply the division lemma to get

43 = 35 x 1 + 8

We consider the new divisor 35 and the new remainder 8,and apply the division lemma to get

35 = 8 x 4 + 3

We consider the new divisor 8 and the new remainder 3,and apply the division lemma to get

8 = 3 x 2 + 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 207 and 578 is 1

Notice that 1 = HCF(2,1) = HCF(3,2) = HCF(8,3) = HCF(35,8) = HCF(43,35) = HCF(164,43) = HCF(207,164) = HCF(578,207) .

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

Step 1: Since 459 > 1, we apply the division lemma to 459 and 1, to get

459 = 1 x 459 + 0

The remainder has now become zero, so our procedure stops. Since the divisor at this stage is 1, the HCF of 1 and 459 is 1

Notice that 1 = HCF(459,1) .

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Frequently Asked Questions on HCF of 207, 578, 459 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 207, 578, 459?

Answer: HCF of 207, 578, 459 is 1 the largest number that divides all the numbers leaving a remainder zero.

3. How to find HCF of 207, 578, 459 using Euclid's Algorithm?

Answer: For arbitrary numbers 207, 578, 459 apply Euclid’s Division Lemma in succession until you obtain a remainder zero. HCF is the remainder in the last but one step.