Highest Common Factor of 495, 7218, 7165 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 495, 7218, 7165 i.e. 1 the largest integer that leaves a remainder zero for all numbers.

HCF of 495, 7218, 7165 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 495, 7218, 7165 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 495, 7218, 7165 is 1.

HCF(495, 7218, 7165) = 1

HCF of 495, 7218, 7165 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 495, 7218, 7165 is 1.

Highest Common Factor of 495,7218,7165 using Euclid's algorithm

Highest Common Factor of 495,7218,7165 is 1

Step 1: Since 7218 > 495, we apply the division lemma to 7218 and 495, to get

7218 = 495 x 14 + 288

Step 2: Since the reminder 495 ≠ 0, we apply division lemma to 288 and 495, to get

495 = 288 x 1 + 207

Step 3: We consider the new divisor 288 and the new remainder 207, and apply the division lemma to get

288 = 207 x 1 + 81

We consider the new divisor 207 and the new remainder 81,and apply the division lemma to get

207 = 81 x 2 + 45

We consider the new divisor 81 and the new remainder 45,and apply the division lemma to get

81 = 45 x 1 + 36

We consider the new divisor 45 and the new remainder 36,and apply the division lemma to get

45 = 36 x 1 + 9

We consider the new divisor 36 and the new remainder 9,and apply the division lemma to get

36 = 9 x 4 + 0

The remainder has now become zero, so our procedure stops. Since the divisor at this stage is 9, the HCF of 495 and 7218 is 9

Notice that 9 = HCF(36,9) = HCF(45,36) = HCF(81,45) = HCF(207,81) = HCF(288,207) = HCF(495,288) = HCF(7218,495) .

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

Step 1: Since 7165 > 9, we apply the division lemma to 7165 and 9, to get

7165 = 9 x 796 + 1

Step 2: Since the reminder 9 ≠ 0, we apply division lemma to 1 and 9, to get

9 = 1 x 9 + 0

The remainder has now become zero, so our procedure stops. Since the divisor at this stage is 1, the HCF of 9 and 7165 is 1

Notice that 1 = HCF(9,1) = HCF(7165,9) .

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Frequently Asked Questions on HCF of 495, 7218, 7165 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 495, 7218, 7165?

Answer: HCF of 495, 7218, 7165 is 1 the largest number that divides all the numbers leaving a remainder zero.

3. How to find HCF of 495, 7218, 7165 using Euclid's Algorithm?

Answer: For arbitrary numbers 495, 7218, 7165 apply Euclid’s Division Lemma in succession until you obtain a remainder zero. HCF is the remainder in the last but one step.