Highest Common Factor of 984, 409, 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 984, 409, 135 i.e. 1 the largest integer that leaves a remainder zero for all numbers.

HCF of 984, 409, 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 984, 409, 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 984, 409, 135 is 1.

HCF(984, 409, 135) = 1

HCF of 984, 409, 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 984, 409, 135 is 1.

Highest Common Factor of 984,409,135 using Euclid's algorithm

Highest Common Factor of 984,409,135 is 1

Step 1: Since 984 > 409, we apply the division lemma to 984 and 409, to get

984 = 409 x 2 + 166

Step 2: Since the reminder 409 ≠ 0, we apply division lemma to 166 and 409, to get

409 = 166 x 2 + 77

Step 3: We consider the new divisor 166 and the new remainder 77, and apply the division lemma to get

166 = 77 x 2 + 12

We consider the new divisor 77 and the new remainder 12,and apply the division lemma to get

77 = 12 x 6 + 5

We consider the new divisor 12 and the new remainder 5,and apply the division lemma to get

12 = 5 x 2 + 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 984 and 409 is 1

Notice that 1 = HCF(2,1) = HCF(5,2) = HCF(12,5) = HCF(77,12) = HCF(166,77) = HCF(409,166) = HCF(984,409) .

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

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

135 = 1 x 135 + 0

The remainder has now become zero, so our procedure stops. Since the divisor at this stage is 1, the HCF of 1 and 135 is 1

Notice that 1 = HCF(135,1) .

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Frequently Asked Questions on HCF of 984, 409, 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 984, 409, 135?

Answer: HCF of 984, 409, 135 is 1 the largest number that divides all the numbers leaving a remainder zero.

3. How to find HCF of 984, 409, 135 using Euclid's Algorithm?

Answer: For arbitrary numbers 984, 409, 135 apply Euclid’s Division Lemma in succession until you obtain a remainder zero. HCF is the remainder in the last but one step.