Highest Common Factor of 584, 916, 404 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 584, 916, 404 i.e. 4 the largest integer that leaves a remainder zero for all numbers.

HCF of 584, 916, 404 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 584, 916, 404 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 584, 916, 404 is 4.

HCF(584, 916, 404) = 4

HCF of 584, 916, 404 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 584, 916, 404 is 4.

Highest Common Factor of 584,916,404 using Euclid's algorithm

Highest Common Factor of 584,916,404 is 4

Step 1: Since 916 > 584, we apply the division lemma to 916 and 584, to get

916 = 584 x 1 + 332

Step 2: Since the reminder 584 ≠ 0, we apply division lemma to 332 and 584, to get

584 = 332 x 1 + 252

Step 3: We consider the new divisor 332 and the new remainder 252, and apply the division lemma to get

332 = 252 x 1 + 80

We consider the new divisor 252 and the new remainder 80,and apply the division lemma to get

252 = 80 x 3 + 12

We consider the new divisor 80 and the new remainder 12,and apply the division lemma to get

80 = 12 x 6 + 8

We consider the new divisor 12 and the new remainder 8,and apply the division lemma to get

12 = 8 x 1 + 4

We consider the new divisor 8 and the new remainder 4,and apply the division lemma to get

8 = 4 x 2 + 0

The remainder has now become zero, so our procedure stops. Since the divisor at this stage is 4, the HCF of 584 and 916 is 4

Notice that 4 = HCF(8,4) = HCF(12,8) = HCF(80,12) = HCF(252,80) = HCF(332,252) = HCF(584,332) = HCF(916,584) .

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

Step 1: Since 404 > 4, we apply the division lemma to 404 and 4, to get

404 = 4 x 101 + 0

The remainder has now become zero, so our procedure stops. Since the divisor at this stage is 4, the HCF of 4 and 404 is 4

Notice that 4 = HCF(404,4) .

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Frequently Asked Questions on HCF of 584, 916, 404 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 584, 916, 404?

Answer: HCF of 584, 916, 404 is 4 the largest number that divides all the numbers leaving a remainder zero.

3. How to find HCF of 584, 916, 404 using Euclid's Algorithm?

Answer: For arbitrary numbers 584, 916, 404 apply Euclid’s Division Lemma in succession until you obtain a remainder zero. HCF is the remainder in the last but one step.