Highest Common Factor of 330, 506, 675 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 330, 506, 675 i.e. 1 the largest integer that leaves a remainder zero for all numbers.

HCF of 330, 506, 675 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 330, 506, 675 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 330, 506, 675 is 1.

HCF(330, 506, 675) = 1

HCF of 330, 506, 675 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 330, 506, 675 is 1.

Highest Common Factor of 330,506,675 using Euclid's algorithm

Highest Common Factor of 330,506,675 is 1

Step 1: Since 506 > 330, we apply the division lemma to 506 and 330, to get

506 = 330 x 1 + 176

Step 2: Since the reminder 330 ≠ 0, we apply division lemma to 176 and 330, to get

330 = 176 x 1 + 154

Step 3: We consider the new divisor 176 and the new remainder 154, and apply the division lemma to get

176 = 154 x 1 + 22

We consider the new divisor 154 and the new remainder 22, and apply the division lemma to get

154 = 22 x 7 + 0

The remainder has now become zero, so our procedure stops. Since the divisor at this stage is 22, the HCF of 330 and 506 is 22

Notice that 22 = HCF(154,22) = HCF(176,154) = HCF(330,176) = HCF(506,330) .

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

Step 1: Since 675 > 22, we apply the division lemma to 675 and 22, to get

675 = 22 x 30 + 15

Step 2: Since the reminder 22 ≠ 0, we apply division lemma to 15 and 22, to get

22 = 15 x 1 + 7

Step 3: We consider the new divisor 15 and the new remainder 7, and apply the division lemma to get

15 = 7 x 2 + 1

We consider the new divisor 7 and the new remainder 1, and apply the division lemma to get

7 = 1 x 7 + 0

The remainder has now become zero, so our procedure stops. Since the divisor at this stage is 1, the HCF of 22 and 675 is 1

Notice that 1 = HCF(7,1) = HCF(15,7) = HCF(22,15) = HCF(675,22) .

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Frequently Asked Questions on HCF of 330, 506, 675 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 330, 506, 675?

Answer: HCF of 330, 506, 675 is 1 the largest number that divides all the numbers leaving a remainder zero.

3. How to find HCF of 330, 506, 675 using Euclid's Algorithm?

Answer: For arbitrary numbers 330, 506, 675 apply Euclid’s Division Lemma in succession until you obtain a remainder zero. HCF is the remainder in the last but one step.