Highest Common Factor of 529, 415, 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 529, 415, 735 i.e. 1 the largest integer that leaves a remainder zero for all numbers.

HCF of 529, 415, 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 529, 415, 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 529, 415, 735 is 1.

HCF(529, 415, 735) = 1

HCF of 529, 415, 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 529, 415, 735 is 1.

Highest Common Factor of 529,415,735 using Euclid's algorithm

Highest Common Factor of 529,415,735 is 1

Step 1: Since 529 > 415, we apply the division lemma to 529 and 415, to get

529 = 415 x 1 + 114

Step 2: Since the reminder 415 ≠ 0, we apply division lemma to 114 and 415, to get

415 = 114 x 3 + 73

Step 3: We consider the new divisor 114 and the new remainder 73, and apply the division lemma to get

114 = 73 x 1 + 41

We consider the new divisor 73 and the new remainder 41,and apply the division lemma to get

73 = 41 x 1 + 32

We consider the new divisor 41 and the new remainder 32,and apply the division lemma to get

41 = 32 x 1 + 9

We consider the new divisor 32 and the new remainder 9,and apply the division lemma to get

32 = 9 x 3 + 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 529 and 415 is 1

Notice that 1 = HCF(4,1) = HCF(5,4) = HCF(9,5) = HCF(32,9) = HCF(41,32) = HCF(73,41) = HCF(114,73) = HCF(415,114) = HCF(529,415) .

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 529, 415, 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 529, 415, 735?

Answer: HCF of 529, 415, 735 is 1 the largest number that divides all the numbers leaving a remainder zero.

3. How to find HCF of 529, 415, 735 using Euclid's Algorithm?

Answer: For arbitrary numbers 529, 415, 735 apply Euclid’s Division Lemma in succession until you obtain a remainder zero. HCF is the remainder in the last but one step.