Highest Common Factor of 96, 64, 313, 226 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 96, 64, 313, 226 i.e. 1 the largest integer that leaves a remainder zero for all numbers.

HCF of 96, 64, 313, 226 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 96, 64, 313, 226 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 96, 64, 313, 226 is 1.

HCF(96, 64, 313, 226) = 1

HCF of 96, 64, 313, 226 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 96, 64, 313, 226 is 1.

Highest Common Factor of 96,64,313,226 using Euclid's algorithm

Highest Common Factor of 96,64,313,226 is 1

Step 1: Since 96 > 64, we apply the division lemma to 96 and 64, to get

96 = 64 x 1 + 32

Step 2: Since the reminder 64 ≠ 0, we apply division lemma to 32 and 64, to get

64 = 32 x 2 + 0

The remainder has now become zero, so our procedure stops. Since the divisor at this stage is 32, the HCF of 96 and 64 is 32

Notice that 32 = HCF(64,32) = HCF(96,64) .

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

Step 1: Since 313 > 32, we apply the division lemma to 313 and 32, to get

313 = 32 x 9 + 25

Step 2: Since the reminder 32 ≠ 0, we apply division lemma to 25 and 32, to get

32 = 25 x 1 + 7

Step 3: We consider the new divisor 25 and the new remainder 7, and apply the division lemma to get

25 = 7 x 3 + 4

We consider the new divisor 7 and the new remainder 4,and apply the division lemma to get

7 = 4 x 1 + 3

We consider the new divisor 4 and the new remainder 3,and apply the division lemma to get

4 = 3 x 1 + 1

We consider the new divisor 3 and the new remainder 1,and apply the division lemma to get

3 = 1 x 3 + 0

The remainder has now become zero, so our procedure stops. Since the divisor at this stage is 1, the HCF of 32 and 313 is 1

Notice that 1 = HCF(3,1) = HCF(4,3) = HCF(7,4) = HCF(25,7) = HCF(32,25) = HCF(313,32) .

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

Step 1: Since 226 > 1, we apply the division lemma to 226 and 1, to get

226 = 1 x 226 + 0

The remainder has now become zero, so our procedure stops. Since the divisor at this stage is 1, the HCF of 1 and 226 is 1

Notice that 1 = HCF(226,1) .

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Frequently Asked Questions on HCF of 96, 64, 313, 226 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 96, 64, 313, 226?

Answer: HCF of 96, 64, 313, 226 is 1 the largest number that divides all the numbers leaving a remainder zero.

3. How to find HCF of 96, 64, 313, 226 using Euclid's Algorithm?

Answer: For arbitrary numbers 96, 64, 313, 226 apply Euclid’s Division Lemma in succession until you obtain a remainder zero. HCF is the remainder in the last but one step.