Highest Common Factor of 529, 735, 364, 40 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, 735, 364, 40 i.e. 1 the largest integer that leaves a remainder zero for all numbers.

HCF of 529, 735, 364, 40 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, 735, 364, 40 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, 735, 364, 40 is 1.

HCF(529, 735, 364, 40) = 1

HCF of 529, 735, 364, 40 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, 735, 364, 40 is 1.

Highest Common Factor of 529,735,364,40 using Euclid's algorithm

Highest Common Factor of 529,735,364,40 is 1

Step 1: Since 735 > 529, we apply the division lemma to 735 and 529, to get

735 = 529 x 1 + 206

Step 2: Since the reminder 529 ≠ 0, we apply division lemma to 206 and 529, to get

529 = 206 x 2 + 117

Step 3: We consider the new divisor 206 and the new remainder 117, and apply the division lemma to get

206 = 117 x 1 + 89

We consider the new divisor 117 and the new remainder 89,and apply the division lemma to get

117 = 89 x 1 + 28

We consider the new divisor 89 and the new remainder 28,and apply the division lemma to get

89 = 28 x 3 + 5

We consider the new divisor 28 and the new remainder 5,and apply the division lemma to get

28 = 5 x 5 + 3

We consider the new divisor 5 and the new remainder 3,and apply the division lemma to get

5 = 3 x 1 + 2

We consider the new divisor 3 and the new remainder 2,and apply the division lemma to get

3 = 2 x 1 + 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 529 and 735 is 1

Notice that 1 = HCF(2,1) = HCF(3,2) = HCF(5,3) = HCF(28,5) = HCF(89,28) = HCF(117,89) = HCF(206,117) = HCF(529,206) = HCF(735,529) .

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

Step 1: Since 364 > 1, we apply the division lemma to 364 and 1, to get

364 = 1 x 364 + 0

The remainder has now become zero, so our procedure stops. Since the divisor at this stage is 1, the HCF of 1 and 364 is 1

Notice that 1 = HCF(364,1) .

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

Step 1: Since 40 > 1, we apply the division lemma to 40 and 1, to get

40 = 1 x 40 + 0

The remainder has now become zero, so our procedure stops. Since the divisor at this stage is 1, the HCF of 1 and 40 is 1

Notice that 1 = HCF(40,1) .

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Frequently Asked Questions on HCF of 529, 735, 364, 40 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, 735, 364, 40?

Answer: HCF of 529, 735, 364, 40 is 1 the largest number that divides all the numbers leaving a remainder zero.

3. How to find HCF of 529, 735, 364, 40 using Euclid's Algorithm?

Answer: For arbitrary numbers 529, 735, 364, 40 apply Euclid’s Division Lemma in succession until you obtain a remainder zero. HCF is the remainder in the last but one step.