Highest Common Factor of 310, 564, 135 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 310, 564, 135 i.e. 1 the largest integer that leaves a remainder zero for all numbers.

HCF of 310, 564, 135 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 310, 564, 135 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 310, 564, 135 is 1.

HCF(310, 564, 135) = 1

HCF of 310, 564, 135 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 310, 564, 135 is 1.

Highest Common Factor of 310,564,135 using Euclid's algorithm

Highest Common Factor of 310,564,135 is 1

Step 1: Since 564 > 310, we apply the division lemma to 564 and 310, to get

564 = 310 x 1 + 254

Step 2: Since the reminder 310 ≠ 0, we apply division lemma to 254 and 310, to get

310 = 254 x 1 + 56

Step 3: We consider the new divisor 254 and the new remainder 56, and apply the division lemma to get

254 = 56 x 4 + 30

We consider the new divisor 56 and the new remainder 30,and apply the division lemma to get

56 = 30 x 1 + 26

We consider the new divisor 30 and the new remainder 26,and apply the division lemma to get

30 = 26 x 1 + 4

We consider the new divisor 26 and the new remainder 4,and apply the division lemma to get

26 = 4 x 6 + 2

We consider the new divisor 4 and the new remainder 2,and apply the division lemma to get

4 = 2 x 2 + 0

The remainder has now become zero, so our procedure stops. Since the divisor at this stage is 2, the HCF of 310 and 564 is 2

Notice that 2 = HCF(4,2) = HCF(26,4) = HCF(30,26) = HCF(56,30) = HCF(254,56) = HCF(310,254) = HCF(564,310) .

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

Step 1: Since 135 > 2, we apply the division lemma to 135 and 2, to get

135 = 2 x 67 + 1

Step 2: Since the reminder 2 ≠ 0, we apply division lemma to 1 and 2, 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 2 and 135 is 1

Notice that 1 = HCF(2,1) = HCF(135,2) .

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Frequently Asked Questions on HCF of 310, 564, 135 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 310, 564, 135?

Answer: HCF of 310, 564, 135 is 1 the largest number that divides all the numbers leaving a remainder zero.

3. How to find HCF of 310, 564, 135 using Euclid's Algorithm?

Answer: For arbitrary numbers 310, 564, 135 apply Euclid’s Division Lemma in succession until you obtain a remainder zero. HCF is the remainder in the last but one step.