Highest Common Factor of 513, 232, 142 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 513, 232, 142 i.e. 1 the largest integer that leaves a remainder zero for all numbers.

HCF of 513, 232, 142 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 513, 232, 142 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 513, 232, 142 is 1.

HCF(513, 232, 142) = 1

HCF of 513, 232, 142 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 513, 232, 142 is 1.

Highest Common Factor of 513,232,142 using Euclid's algorithm

Highest Common Factor of 513,232,142 is 1

Step 1: Since 513 > 232, we apply the division lemma to 513 and 232, to get

513 = 232 x 2 + 49

Step 2: Since the reminder 232 ≠ 0, we apply division lemma to 49 and 232, to get

232 = 49 x 4 + 36

Step 3: We consider the new divisor 49 and the new remainder 36, and apply the division lemma to get

49 = 36 x 1 + 13

We consider the new divisor 36 and the new remainder 13,and apply the division lemma to get

36 = 13 x 2 + 10

We consider the new divisor 13 and the new remainder 10,and apply the division lemma to get

13 = 10 x 1 + 3

We consider the new divisor 10 and the new remainder 3,and apply the division lemma to get

10 = 3 x 3 + 1

We consider the new divisor 3 and the new remainder 1,and apply the division lemma 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 513 and 232 is 1

Notice that 1 = HCF(3,1) = HCF(10,3) = HCF(13,10) = HCF(36,13) = HCF(49,36) = HCF(232,49) = HCF(513,232) .

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

Step 1: Since 142 > 1, we apply the division lemma to 142 and 1, to get

142 = 1 x 142 + 0

The remainder has now become zero, so our procedure stops. Since the divisor at this stage is 1, the HCF of 1 and 142 is 1

Notice that 1 = HCF(142,1) .

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Frequently Asked Questions on HCF of 513, 232, 142 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 513, 232, 142?

Answer: HCF of 513, 232, 142 is 1 the largest number that divides all the numbers leaving a remainder zero.

3. How to find HCF of 513, 232, 142 using Euclid's Algorithm?

Answer: For arbitrary numbers 513, 232, 142 apply Euclid’s Division Lemma in succession until you obtain a remainder zero. HCF is the remainder in the last but one step.