Highest Common Factor of 313, 5924, 5662 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 313, 5924, 5662 i.e. 1 the largest integer that leaves a remainder zero for all numbers.

HCF of 313, 5924, 5662 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 313, 5924, 5662 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 313, 5924, 5662 is 1.

HCF(313, 5924, 5662) = 1

HCF of 313, 5924, 5662 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 313, 5924, 5662 is 1.

Highest Common Factor of 313,5924,5662 using Euclid's algorithm

Highest Common Factor of 313,5924,5662 is 1

Step 1: Since 5924 > 313, we apply the division lemma to 5924 and 313, to get

5924 = 313 x 18 + 290

Step 2: Since the reminder 313 ≠ 0, we apply division lemma to 290 and 313, to get

313 = 290 x 1 + 23

Step 3: We consider the new divisor 290 and the new remainder 23, and apply the division lemma to get

290 = 23 x 12 + 14

We consider the new divisor 23 and the new remainder 14,and apply the division lemma to get

23 = 14 x 1 + 9

We consider the new divisor 14 and the new remainder 9,and apply the division lemma to get

14 = 9 x 1 + 5

We consider the new divisor 9 and the new remainder 5,and apply the division lemma to get

9 = 5 x 1 + 4

We consider the new divisor 5 and the new remainder 4,and apply the division lemma to get

5 = 4 x 1 + 1

We consider the new divisor 4 and the new remainder 1,and apply the division lemma to get

4 = 1 x 4 + 0

The remainder has now become zero, so our procedure stops. Since the divisor at this stage is 1, the HCF of 313 and 5924 is 1

Notice that 1 = HCF(4,1) = HCF(5,4) = HCF(9,5) = HCF(14,9) = HCF(23,14) = HCF(290,23) = HCF(313,290) = HCF(5924,313) .

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

Step 1: Since 5662 > 1, we apply the division lemma to 5662 and 1, to get

5662 = 1 x 5662 + 0

The remainder has now become zero, so our procedure stops. Since the divisor at this stage is 1, the HCF of 1 and 5662 is 1

Notice that 1 = HCF(5662,1) .

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Frequently Asked Questions on HCF of 313, 5924, 5662 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 313, 5924, 5662?

Answer: HCF of 313, 5924, 5662 is 1 the largest number that divides all the numbers leaving a remainder zero.

3. How to find HCF of 313, 5924, 5662 using Euclid's Algorithm?

Answer: For arbitrary numbers 313, 5924, 5662 apply Euclid’s Division Lemma in succession until you obtain a remainder zero. HCF is the remainder in the last but one step.