Highest Common Factor of 509, 321, 688 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 509, 321, 688 i.e. 1 the largest integer that leaves a remainder zero for all numbers.

HCF of 509, 321, 688 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 509, 321, 688 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 509, 321, 688 is 1.

HCF(509, 321, 688) = 1

HCF of 509, 321, 688 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 509, 321, 688 is 1.

Highest Common Factor of 509,321,688 using Euclid's algorithm

Highest Common Factor of 509,321,688 is 1

Step 1: Since 509 > 321, we apply the division lemma to 509 and 321, to get

509 = 321 x 1 + 188

Step 2: Since the reminder 321 ≠ 0, we apply division lemma to 188 and 321, to get

321 = 188 x 1 + 133

Step 3: We consider the new divisor 188 and the new remainder 133, and apply the division lemma to get

188 = 133 x 1 + 55

We consider the new divisor 133 and the new remainder 55,and apply the division lemma to get

133 = 55 x 2 + 23

We consider the new divisor 55 and the new remainder 23,and apply the division lemma to get

55 = 23 x 2 + 9

We consider the new divisor 23 and the new remainder 9,and apply the division lemma to get

23 = 9 x 2 + 5

We consider the new divisor 9 and the new remainder 5,and apply the division lemma to get

9 = 5 x 1 + 4

We consider the new divisor 5 and the new remainder 4,and apply the division lemma to get

5 = 4 x 1 + 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 509 and 321 is 1

Notice that 1 = HCF(4,1) = HCF(5,4) = HCF(9,5) = HCF(23,9) = HCF(55,23) = HCF(133,55) = HCF(188,133) = HCF(321,188) = HCF(509,321) .

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

Step 1: Since 688 > 1, we apply the division lemma to 688 and 1, to get

688 = 1 x 688 + 0

The remainder has now become zero, so our procedure stops. Since the divisor at this stage is 1, the HCF of 1 and 688 is 1

Notice that 1 = HCF(688,1) .

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Frequently Asked Questions on HCF of 509, 321, 688 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 509, 321, 688?

Answer: HCF of 509, 321, 688 is 1 the largest number that divides all the numbers leaving a remainder zero.

3. How to find HCF of 509, 321, 688 using Euclid's Algorithm?

Answer: For arbitrary numbers 509, 321, 688 apply Euclid’s Division Lemma in succession until you obtain a remainder zero. HCF is the remainder in the last but one step.