Highest Common Factor of 321, 825, 652 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 321, 825, 652 i.e. 1 the largest integer that leaves a remainder zero for all numbers.

HCF of 321, 825, 652 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 321, 825, 652 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 321, 825, 652 is 1.

HCF(321, 825, 652) = 1

HCF of 321, 825, 652 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 321, 825, 652 is 1.

Highest Common Factor of 321,825,652 using Euclid's algorithm

Highest Common Factor of 321,825,652 is 1

Step 1: Since 825 > 321, we apply the division lemma to 825 and 321, to get

825 = 321 x 2 + 183

Step 2: Since the reminder 321 ≠ 0, we apply division lemma to 183 and 321, to get

321 = 183 x 1 + 138

Step 3: We consider the new divisor 183 and the new remainder 138, and apply the division lemma to get

183 = 138 x 1 + 45

We consider the new divisor 138 and the new remainder 45,and apply the division lemma to get

138 = 45 x 3 + 3

We consider the new divisor 45 and the new remainder 3,and apply the division lemma to get

45 = 3 x 15 + 0

The remainder has now become zero, so our procedure stops. Since the divisor at this stage is 3, the HCF of 321 and 825 is 3

Notice that 3 = HCF(45,3) = HCF(138,45) = HCF(183,138) = HCF(321,183) = HCF(825,321) .

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

Step 1: Since 652 > 3, we apply the division lemma to 652 and 3, to get

652 = 3 x 217 + 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 652 is 1

Notice that 1 = HCF(3,1) = HCF(652,3) .

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Frequently Asked Questions on HCF of 321, 825, 652 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 321, 825, 652?

Answer: HCF of 321, 825, 652 is 1 the largest number that divides all the numbers leaving a remainder zero.

3. How to find HCF of 321, 825, 652 using Euclid's Algorithm?

Answer: For arbitrary numbers 321, 825, 652 apply Euclid’s Division Lemma in succession until you obtain a remainder zero. HCF is the remainder in the last but one step.