Highest Common Factor of 552, 305, 735 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 552, 305, 735 i.e. 1 the largest integer that leaves a remainder zero for all numbers.

HCF of 552, 305, 735 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 552, 305, 735 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 552, 305, 735 is 1.

HCF(552, 305, 735) = 1

HCF of 552, 305, 735 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 552, 305, 735 is 1.

Highest Common Factor of 552,305,735 using Euclid's algorithm

Highest Common Factor of 552,305,735 is 1

Step 1: Since 552 > 305, we apply the division lemma to 552 and 305, to get

552 = 305 x 1 + 247

Step 2: Since the reminder 305 ≠ 0, we apply division lemma to 247 and 305, to get

305 = 247 x 1 + 58

Step 3: We consider the new divisor 247 and the new remainder 58, and apply the division lemma to get

247 = 58 x 4 + 15

We consider the new divisor 58 and the new remainder 15,and apply the division lemma to get

58 = 15 x 3 + 13

We consider the new divisor 15 and the new remainder 13,and apply the division lemma to get

15 = 13 x 1 + 2

We consider the new divisor 13 and the new remainder 2,and apply the division lemma to get

13 = 2 x 6 + 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 552 and 305 is 1

Notice that 1 = HCF(2,1) = HCF(13,2) = HCF(15,13) = HCF(58,15) = HCF(247,58) = HCF(305,247) = HCF(552,305) .

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

Step 1: Since 735 > 1, we apply the division lemma to 735 and 1, to get

735 = 1 x 735 + 0

The remainder has now become zero, so our procedure stops. Since the divisor at this stage is 1, the HCF of 1 and 735 is 1

Notice that 1 = HCF(735,1) .

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Frequently Asked Questions on HCF of 552, 305, 735 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 552, 305, 735?

Answer: HCF of 552, 305, 735 is 1 the largest number that divides all the numbers leaving a remainder zero.

3. How to find HCF of 552, 305, 735 using Euclid's Algorithm?

Answer: For arbitrary numbers 552, 305, 735 apply Euclid’s Division Lemma in succession until you obtain a remainder zero. HCF is the remainder in the last but one step.