Highest Common Factor of 540, 945, 908 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 540, 945, 908 i.e. 1 the largest integer that leaves a remainder zero for all numbers.

HCF of 540, 945, 908 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 540, 945, 908 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 540, 945, 908 is 1.

HCF(540, 945, 908) = 1

HCF of 540, 945, 908 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 540, 945, 908 is 1.

Highest Common Factor of 540,945,908 using Euclid's algorithm

Highest Common Factor of 540,945,908 is 1

Step 1: Since 945 > 540, we apply the division lemma to 945 and 540, to get

945 = 540 x 1 + 405

Step 2: Since the reminder 540 ≠ 0, we apply division lemma to 405 and 540, to get

540 = 405 x 1 + 135

Step 3: We consider the new divisor 405 and the new remainder 135, and apply the division lemma to get

405 = 135 x 3 + 0

The remainder has now become zero, so our procedure stops. Since the divisor at this stage is 135, the HCF of 540 and 945 is 135

Notice that 135 = HCF(405,135) = HCF(540,405) = HCF(945,540) .

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

Step 1: Since 908 > 135, we apply the division lemma to 908 and 135, to get

908 = 135 x 6 + 98

Step 2: Since the reminder 135 ≠ 0, we apply division lemma to 98 and 135, to get

135 = 98 x 1 + 37

Step 3: We consider the new divisor 98 and the new remainder 37, and apply the division lemma to get

98 = 37 x 2 + 24

We consider the new divisor 37 and the new remainder 24,and apply the division lemma to get

37 = 24 x 1 + 13

We consider the new divisor 24 and the new remainder 13,and apply the division lemma to get

24 = 13 x 1 + 11

We consider the new divisor 13 and the new remainder 11,and apply the division lemma to get

13 = 11 x 1 + 2

We consider the new divisor 11 and the new remainder 2,and apply the division lemma to get

11 = 2 x 5 + 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 908 is 1

Notice that 1 = HCF(2,1) = HCF(11,2) = HCF(13,11) = HCF(24,13) = HCF(37,24) = HCF(98,37) = HCF(135,98) = HCF(908,135) .

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Frequently Asked Questions on HCF of 540, 945, 908 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 540, 945, 908?

Answer: HCF of 540, 945, 908 is 1 the largest number that divides all the numbers leaving a remainder zero.

3. How to find HCF of 540, 945, 908 using Euclid's Algorithm?

Answer: For arbitrary numbers 540, 945, 908 apply Euclid’s Division Lemma in succession until you obtain a remainder zero. HCF is the remainder in the last but one step.