Highest Common Factor of 135, 838, 954 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 135, 838, 954 i.e. 1 the largest integer that leaves a remainder zero for all numbers.

HCF of 135, 838, 954 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 135, 838, 954 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 135, 838, 954 is 1.

HCF(135, 838, 954) = 1

HCF of 135, 838, 954 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 135, 838, 954 is 1.

Highest Common Factor of 135,838,954 using Euclid's algorithm

Highest Common Factor of 135,838,954 is 1

Step 1: Since 838 > 135, we apply the division lemma to 838 and 135, to get

838 = 135 x 6 + 28

Step 2: Since the reminder 135 ≠ 0, we apply division lemma to 28 and 135, to get

135 = 28 x 4 + 23

Step 3: We consider the new divisor 28 and the new remainder 23, and apply the division lemma to get

28 = 23 x 1 + 5

We consider the new divisor 23 and the new remainder 5,and apply the division lemma to get

23 = 5 x 4 + 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 135 and 838 is 1

Notice that 1 = HCF(2,1) = HCF(3,2) = HCF(5,3) = HCF(23,5) = HCF(28,23) = HCF(135,28) = HCF(838,135) .

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

Step 1: Since 954 > 1, we apply the division lemma to 954 and 1, to get

954 = 1 x 954 + 0

The remainder has now become zero, so our procedure stops. Since the divisor at this stage is 1, the HCF of 1 and 954 is 1

Notice that 1 = HCF(954,1) .

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Frequently Asked Questions on HCF of 135, 838, 954 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 135, 838, 954?

Answer: HCF of 135, 838, 954 is 1 the largest number that divides all the numbers leaving a remainder zero.

3. How to find HCF of 135, 838, 954 using Euclid's Algorithm?

Answer: For arbitrary numbers 135, 838, 954 apply Euclid’s Division Lemma in succession until you obtain a remainder zero. HCF is the remainder in the last but one step.