Highest Common Factor of 370, 652, 324 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 370, 652, 324 i.e. 2 the largest integer that leaves a remainder zero for all numbers.

HCF of 370, 652, 324 is 2 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 370, 652, 324 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 370, 652, 324 is 2.

HCF(370, 652, 324) = 2

HCF of 370, 652, 324 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 370, 652, 324 is 2.

Highest Common Factor of 370,652,324 using Euclid's algorithm

Highest Common Factor of 370,652,324 is 2

Step 1: Since 652 > 370, we apply the division lemma to 652 and 370, to get

652 = 370 x 1 + 282

Step 2: Since the reminder 370 ≠ 0, we apply division lemma to 282 and 370, to get

370 = 282 x 1 + 88

Step 3: We consider the new divisor 282 and the new remainder 88, and apply the division lemma to get

282 = 88 x 3 + 18

We consider the new divisor 88 and the new remainder 18,and apply the division lemma to get

88 = 18 x 4 + 16

We consider the new divisor 18 and the new remainder 16,and apply the division lemma to get

18 = 16 x 1 + 2

We consider the new divisor 16 and the new remainder 2,and apply the division lemma to get

16 = 2 x 8 + 0

The remainder has now become zero, so our procedure stops. Since the divisor at this stage is 2, the HCF of 370 and 652 is 2

Notice that 2 = HCF(16,2) = HCF(18,16) = HCF(88,18) = HCF(282,88) = HCF(370,282) = HCF(652,370) .

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

Step 1: Since 324 > 2, we apply the division lemma to 324 and 2, to get

324 = 2 x 162 + 0

The remainder has now become zero, so our procedure stops. Since the divisor at this stage is 2, the HCF of 2 and 324 is 2

Notice that 2 = HCF(324,2) .

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Frequently Asked Questions on HCF of 370, 652, 324 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 370, 652, 324?

Answer: HCF of 370, 652, 324 is 2 the largest number that divides all the numbers leaving a remainder zero.

3. How to find HCF of 370, 652, 324 using Euclid's Algorithm?

Answer: For arbitrary numbers 370, 652, 324 apply Euclid’s Division Lemma in succession until you obtain a remainder zero. HCF is the remainder in the last but one step.