Highest Common Factor of 3630, 8669, 37040 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 3630, 8669, 37040 i.e. 1 the largest integer that leaves a remainder zero for all numbers.

HCF of 3630, 8669, 37040 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 3630, 8669, 37040 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 3630, 8669, 37040 is 1.

HCF(3630, 8669, 37040) = 1

HCF of 3630, 8669, 37040 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 3630, 8669, 37040 is 1.

Highest Common Factor of 3630,8669,37040 using Euclid's algorithm

Highest Common Factor of 3630,8669,37040 is 1

Step 1: Since 8669 > 3630, we apply the division lemma to 8669 and 3630, to get

8669 = 3630 x 2 + 1409

Step 2: Since the reminder 3630 ≠ 0, we apply division lemma to 1409 and 3630, to get

3630 = 1409 x 2 + 812

Step 3: We consider the new divisor 1409 and the new remainder 812, and apply the division lemma to get

1409 = 812 x 1 + 597

We consider the new divisor 812 and the new remainder 597,and apply the division lemma to get

812 = 597 x 1 + 215

We consider the new divisor 597 and the new remainder 215,and apply the division lemma to get

597 = 215 x 2 + 167

We consider the new divisor 215 and the new remainder 167,and apply the division lemma to get

215 = 167 x 1 + 48

We consider the new divisor 167 and the new remainder 48,and apply the division lemma to get

167 = 48 x 3 + 23

We consider the new divisor 48 and the new remainder 23,and apply the division lemma to get

48 = 23 x 2 + 2

We consider the new divisor 23 and the new remainder 2,and apply the division lemma to get

23 = 2 x 11 + 1

We consider the new divisor 2 and the new remainder 1,and apply the division lemma to get

2 = 1 x 2 + 0

The remainder has now become zero, so our procedure stops. Since the divisor at this stage is 1, the HCF of 3630 and 8669 is 1

Notice that 1 = HCF(2,1) = HCF(23,2) = HCF(48,23) = HCF(167,48) = HCF(215,167) = HCF(597,215) = HCF(812,597) = HCF(1409,812) = HCF(3630,1409) = HCF(8669,3630) .

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

Step 1: Since 37040 > 1, we apply the division lemma to 37040 and 1, to get

37040 = 1 x 37040 + 0

The remainder has now become zero, so our procedure stops. Since the divisor at this stage is 1, the HCF of 1 and 37040 is 1

Notice that 1 = HCF(37040,1) .

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Frequently Asked Questions on HCF of 3630, 8669, 37040 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 3630, 8669, 37040?

Answer: HCF of 3630, 8669, 37040 is 1 the largest number that divides all the numbers leaving a remainder zero.

3. How to find HCF of 3630, 8669, 37040 using Euclid's Algorithm?

Answer: For arbitrary numbers 3630, 8669, 37040 apply Euclid’s Division Lemma in succession until you obtain a remainder zero. HCF is the remainder in the last but one step.