Highest Common Factor of 675, 984, 19 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 675, 984, 19 i.e. 1 the largest integer that leaves a remainder zero for all numbers.

HCF of 675, 984, 19 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 675, 984, 19 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 675, 984, 19 is 1.

HCF(675, 984, 19) = 1

HCF of 675, 984, 19 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 675, 984, 19 is 1.

Highest Common Factor of 675,984,19 using Euclid's algorithm

Highest Common Factor of 675,984,19 is 1

Step 1: Since 984 > 675, we apply the division lemma to 984 and 675, to get

984 = 675 x 1 + 309

Step 2: Since the reminder 675 ≠ 0, we apply division lemma to 309 and 675, to get

675 = 309 x 2 + 57

Step 3: We consider the new divisor 309 and the new remainder 57, and apply the division lemma to get

309 = 57 x 5 + 24

We consider the new divisor 57 and the new remainder 24,and apply the division lemma to get

57 = 24 x 2 + 9

We consider the new divisor 24 and the new remainder 9,and apply the division lemma to get

24 = 9 x 2 + 6

We consider the new divisor 9 and the new remainder 6,and apply the division lemma to get

9 = 6 x 1 + 3

We consider the new divisor 6 and the new remainder 3,and apply the division lemma to get

6 = 3 x 2 + 0

The remainder has now become zero, so our procedure stops. Since the divisor at this stage is 3, the HCF of 675 and 984 is 3

Notice that 3 = HCF(6,3) = HCF(9,6) = HCF(24,9) = HCF(57,24) = HCF(309,57) = HCF(675,309) = HCF(984,675) .

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

Step 1: Since 19 > 3, we apply the division lemma to 19 and 3, to get

19 = 3 x 6 + 1

Step 2: Since the reminder 3 ≠ 0, we apply division lemma to 1 and 3, to get

3 = 1 x 3 + 0

The remainder has now become zero, so our procedure stops. Since the divisor at this stage is 1, the HCF of 3 and 19 is 1

Notice that 1 = HCF(3,1) = HCF(19,3) .

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Frequently Asked Questions on HCF of 675, 984, 19 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 675, 984, 19?

Answer: HCF of 675, 984, 19 is 1 the largest number that divides all the numbers leaving a remainder zero.

3. How to find HCF of 675, 984, 19 using Euclid's Algorithm?

Answer: For arbitrary numbers 675, 984, 19 apply Euclid’s Division Lemma in succession until you obtain a remainder zero. HCF is the remainder in the last but one step.