Highest Common Factor of 369, 514, 15 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 369, 514, 15 i.e. 1 the largest integer that leaves a remainder zero for all numbers.

HCF of 369, 514, 15 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 369, 514, 15 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 369, 514, 15 is 1.

HCF(369, 514, 15) = 1

HCF of 369, 514, 15 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 369, 514, 15 is 1.

Highest Common Factor of 369,514,15 using Euclid's algorithm

Highest Common Factor of 369,514,15 is 1

Step 1: Since 514 > 369, we apply the division lemma to 514 and 369, to get

514 = 369 x 1 + 145

Step 2: Since the reminder 369 ≠ 0, we apply division lemma to 145 and 369, to get

369 = 145 x 2 + 79

Step 3: We consider the new divisor 145 and the new remainder 79, and apply the division lemma to get

145 = 79 x 1 + 66

We consider the new divisor 79 and the new remainder 66,and apply the division lemma to get

79 = 66 x 1 + 13

We consider the new divisor 66 and the new remainder 13,and apply the division lemma to get

66 = 13 x 5 + 1

We consider the new divisor 13 and the new remainder 1,and apply the division lemma to get

13 = 1 x 13 + 0

The remainder has now become zero, so our procedure stops. Since the divisor at this stage is 1, the HCF of 369 and 514 is 1

Notice that 1 = HCF(13,1) = HCF(66,13) = HCF(79,66) = HCF(145,79) = HCF(369,145) = HCF(514,369) .

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

Step 1: Since 15 > 1, we apply the division lemma to 15 and 1, to get

15 = 1 x 15 + 0

The remainder has now become zero, so our procedure stops. Since the divisor at this stage is 1, the HCF of 1 and 15 is 1

Notice that 1 = HCF(15,1) .

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Frequently Asked Questions on HCF of 369, 514, 15 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 369, 514, 15?

Answer: HCF of 369, 514, 15 is 1 the largest number that divides all the numbers leaving a remainder zero.

3. How to find HCF of 369, 514, 15 using Euclid's Algorithm?

Answer: For arbitrary numbers 369, 514, 15 apply Euclid’s Division Lemma in succession until you obtain a remainder zero. HCF is the remainder in the last but one step.