Highest Common Factor of 240, 102, 509 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 240, 102, 509 i.e. 1 the largest integer that leaves a remainder zero for all numbers.

HCF of 240, 102, 509 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 240, 102, 509 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 240, 102, 509 is 1.

HCF(240, 102, 509) = 1

HCF of 240, 102, 509 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 240, 102, 509 is 1.

Highest Common Factor of 240,102,509 using Euclid's algorithm

Highest Common Factor of 240,102,509 is 1

Step 1: Since 240 > 102, we apply the division lemma to 240 and 102, to get

240 = 102 x 2 + 36

Step 2: Since the reminder 102 ≠ 0, we apply division lemma to 36 and 102, to get

102 = 36 x 2 + 30

Step 3: We consider the new divisor 36 and the new remainder 30, and apply the division lemma to get

36 = 30 x 1 + 6

We consider the new divisor 30 and the new remainder 6, and apply the division lemma to get

30 = 6 x 5 + 0

The remainder has now become zero, so our procedure stops. Since the divisor at this stage is 6, the HCF of 240 and 102 is 6

Notice that 6 = HCF(30,6) = HCF(36,30) = HCF(102,36) = HCF(240,102) .

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

Step 1: Since 509 > 6, we apply the division lemma to 509 and 6, to get

509 = 6 x 84 + 5

Step 2: Since the reminder 6 ≠ 0, we apply division lemma to 5 and 6, to get

6 = 5 x 1 + 1

Step 3: We consider the new divisor 5 and the new remainder 1, and apply the division lemma to get

5 = 1 x 5 + 0

The remainder has now become zero, so our procedure stops. Since the divisor at this stage is 1, the HCF of 6 and 509 is 1

Notice that 1 = HCF(5,1) = HCF(6,5) = HCF(509,6) .

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Frequently Asked Questions on HCF of 240, 102, 509 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 240, 102, 509?

Answer: HCF of 240, 102, 509 is 1 the largest number that divides all the numbers leaving a remainder zero.

3. How to find HCF of 240, 102, 509 using Euclid's Algorithm?

Answer: For arbitrary numbers 240, 102, 509 apply Euclid’s Division Lemma in succession until you obtain a remainder zero. HCF is the remainder in the last but one step.