Highest Common Factor of 512, 741, 116 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 512, 741, 116 i.e. 1 the largest integer that leaves a remainder zero for all numbers.

HCF of 512, 741, 116 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 512, 741, 116 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 512, 741, 116 is 1.

HCF(512, 741, 116) = 1

HCF of 512, 741, 116 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 512, 741, 116 is 1.

Highest Common Factor of 512,741,116 using Euclid's algorithm

Highest Common Factor of 512,741,116 is 1

Step 1: Since 741 > 512, we apply the division lemma to 741 and 512, to get

741 = 512 x 1 + 229

Step 2: Since the reminder 512 ≠ 0, we apply division lemma to 229 and 512, to get

512 = 229 x 2 + 54

Step 3: We consider the new divisor 229 and the new remainder 54, and apply the division lemma to get

229 = 54 x 4 + 13

We consider the new divisor 54 and the new remainder 13,and apply the division lemma to get

54 = 13 x 4 + 2

We consider the new divisor 13 and the new remainder 2,and apply the division lemma to get

13 = 2 x 6 + 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 512 and 741 is 1

Notice that 1 = HCF(2,1) = HCF(13,2) = HCF(54,13) = HCF(229,54) = HCF(512,229) = HCF(741,512) .

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

Step 1: Since 116 > 1, we apply the division lemma to 116 and 1, to get

116 = 1 x 116 + 0

The remainder has now become zero, so our procedure stops. Since the divisor at this stage is 1, the HCF of 1 and 116 is 1

Notice that 1 = HCF(116,1) .

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Frequently Asked Questions on HCF of 512, 741, 116 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 512, 741, 116?

Answer: HCF of 512, 741, 116 is 1 the largest number that divides all the numbers leaving a remainder zero.

3. How to find HCF of 512, 741, 116 using Euclid's Algorithm?

Answer: For arbitrary numbers 512, 741, 116 apply Euclid’s Division Lemma in succession until you obtain a remainder zero. HCF is the remainder in the last but one step.