Highest Common Factor of 5354, 7055, 31216 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 5354, 7055, 31216 i.e. 1 the largest integer that leaves a remainder zero for all numbers.

HCF of 5354, 7055, 31216 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 5354, 7055, 31216 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 5354, 7055, 31216 is 1.

HCF(5354, 7055, 31216) = 1

HCF of 5354, 7055, 31216 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 5354, 7055, 31216 is 1.

Highest Common Factor of 5354,7055,31216 using Euclid's algorithm

Highest Common Factor of 5354,7055,31216 is 1

Step 1: Since 7055 > 5354, we apply the division lemma to 7055 and 5354, to get

7055 = 5354 x 1 + 1701

Step 2: Since the reminder 5354 ≠ 0, we apply division lemma to 1701 and 5354, to get

5354 = 1701 x 3 + 251

Step 3: We consider the new divisor 1701 and the new remainder 251, and apply the division lemma to get

1701 = 251 x 6 + 195

We consider the new divisor 251 and the new remainder 195,and apply the division lemma to get

251 = 195 x 1 + 56

We consider the new divisor 195 and the new remainder 56,and apply the division lemma to get

195 = 56 x 3 + 27

We consider the new divisor 56 and the new remainder 27,and apply the division lemma to get

56 = 27 x 2 + 2

We consider the new divisor 27 and the new remainder 2,and apply the division lemma to get

27 = 2 x 13 + 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 5354 and 7055 is 1

Notice that 1 = HCF(2,1) = HCF(27,2) = HCF(56,27) = HCF(195,56) = HCF(251,195) = HCF(1701,251) = HCF(5354,1701) = HCF(7055,5354) .

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

Step 1: Since 31216 > 1, we apply the division lemma to 31216 and 1, to get

31216 = 1 x 31216 + 0

The remainder has now become zero, so our procedure stops. Since the divisor at this stage is 1, the HCF of 1 and 31216 is 1

Notice that 1 = HCF(31216,1) .

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Frequently Asked Questions on HCF of 5354, 7055, 31216 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 5354, 7055, 31216?

Answer: HCF of 5354, 7055, 31216 is 1 the largest number that divides all the numbers leaving a remainder zero.

3. How to find HCF of 5354, 7055, 31216 using Euclid's Algorithm?

Answer: For arbitrary numbers 5354, 7055, 31216 apply Euclid’s Division Lemma in succession until you obtain a remainder zero. HCF is the remainder in the last but one step.