Highest Common Factor of 529, 409, 902 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, 409, 902 i.e. 1 the largest integer that leaves a remainder zero for all numbers.

HCF of 529, 409, 902 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, 409, 902 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, 409, 902 is 1.

HCF(529, 409, 902) = 1

HCF of 529, 409, 902 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, 409, 902 is 1.

Highest Common Factor of 529,409,902 using Euclid's algorithm

Highest Common Factor of 529,409,902 is 1

Step 1: Since 529 > 409, we apply the division lemma to 529 and 409, to get

529 = 409 x 1 + 120

Step 2: Since the reminder 409 ≠ 0, we apply division lemma to 120 and 409, to get

409 = 120 x 3 + 49

Step 3: We consider the new divisor 120 and the new remainder 49, and apply the division lemma to get

120 = 49 x 2 + 22

We consider the new divisor 49 and the new remainder 22,and apply the division lemma to get

49 = 22 x 2 + 5

We consider the new divisor 22 and the new remainder 5,and apply the division lemma to get

22 = 5 x 4 + 2

We consider the new divisor 5 and the new remainder 2,and apply the division lemma to get

5 = 2 x 2 + 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 409 is 1

Notice that 1 = HCF(2,1) = HCF(5,2) = HCF(22,5) = HCF(49,22) = HCF(120,49) = HCF(409,120) = HCF(529,409) .

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

Step 1: Since 902 > 1, we apply the division lemma to 902 and 1, to get

902 = 1 x 902 + 0

The remainder has now become zero, so our procedure stops. Since the divisor at this stage is 1, the HCF of 1 and 902 is 1

Notice that 1 = HCF(902,1) .

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Frequently Asked Questions on HCF of 529, 409, 902 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, 409, 902?

Answer: HCF of 529, 409, 902 is 1 the largest number that divides all the numbers leaving a remainder zero.

3. How to find HCF of 529, 409, 902 using Euclid's Algorithm?

Answer: For arbitrary numbers 529, 409, 902 apply Euclid’s Division Lemma in succession until you obtain a remainder zero. HCF is the remainder in the last but one step.