Highest Common Factor of 512, 900, 416 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, 900, 416 i.e. 4 the largest integer that leaves a remainder zero for all numbers.

HCF of 512, 900, 416 is 4 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, 900, 416 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, 900, 416 is 4.

HCF(512, 900, 416) = 4

HCF of 512, 900, 416 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, 900, 416 is 4.

Highest Common Factor of 512,900,416 using Euclid's algorithm

Highest Common Factor of 512,900,416 is 4

Step 1: Since 900 > 512, we apply the division lemma to 900 and 512, to get

900 = 512 x 1 + 388

Step 2: Since the reminder 512 ≠ 0, we apply division lemma to 388 and 512, to get

512 = 388 x 1 + 124

Step 3: We consider the new divisor 388 and the new remainder 124, and apply the division lemma to get

388 = 124 x 3 + 16

We consider the new divisor 124 and the new remainder 16,and apply the division lemma to get

124 = 16 x 7 + 12

We consider the new divisor 16 and the new remainder 12,and apply the division lemma to get

16 = 12 x 1 + 4

We consider the new divisor 12 and the new remainder 4,and apply the division lemma to get

12 = 4 x 3 + 0

The remainder has now become zero, so our procedure stops. Since the divisor at this stage is 4, the HCF of 512 and 900 is 4

Notice that 4 = HCF(12,4) = HCF(16,12) = HCF(124,16) = HCF(388,124) = HCF(512,388) = HCF(900,512) .

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

Step 1: Since 416 > 4, we apply the division lemma to 416 and 4, to get

416 = 4 x 104 + 0

The remainder has now become zero, so our procedure stops. Since the divisor at this stage is 4, the HCF of 4 and 416 is 4

Notice that 4 = HCF(416,4) .

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Frequently Asked Questions on HCF of 512, 900, 416 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, 900, 416?

Answer: HCF of 512, 900, 416 is 4 the largest number that divides all the numbers leaving a remainder zero.

3. How to find HCF of 512, 900, 416 using Euclid's Algorithm?

Answer: For arbitrary numbers 512, 900, 416 apply Euclid’s Division Lemma in succession until you obtain a remainder zero. HCF is the remainder in the last but one step.