Highest Common Factor of 803, 584, 908, 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 803, 584, 908, 135 i.e. 1 the largest integer that leaves a remainder zero for all numbers.

HCF of 803, 584, 908, 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 803, 584, 908, 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 803, 584, 908, 135 is 1.

HCF(803, 584, 908, 135) = 1

HCF of 803, 584, 908, 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 803, 584, 908, 135 is 1.

Highest Common Factor of 803,584,908,135 using Euclid's algorithm

Highest Common Factor of 803,584,908,135 is 1

Step 1: Since 803 > 584, we apply the division lemma to 803 and 584, to get

803 = 584 x 1 + 219

Step 2: Since the reminder 584 ≠ 0, we apply division lemma to 219 and 584, to get

584 = 219 x 2 + 146

Step 3: We consider the new divisor 219 and the new remainder 146, and apply the division lemma to get

219 = 146 x 1 + 73

We consider the new divisor 146 and the new remainder 73, and apply the division lemma to get

146 = 73 x 2 + 0

The remainder has now become zero, so our procedure stops. Since the divisor at this stage is 73, the HCF of 803 and 584 is 73

Notice that 73 = HCF(146,73) = HCF(219,146) = HCF(584,219) = HCF(803,584) .

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

Step 1: Since 908 > 73, we apply the division lemma to 908 and 73, to get

908 = 73 x 12 + 32

Step 2: Since the reminder 73 ≠ 0, we apply division lemma to 32 and 73, to get

73 = 32 x 2 + 9

Step 3: We consider the new divisor 32 and the new remainder 9, and apply the division lemma to get

32 = 9 x 3 + 5

We consider the new divisor 9 and the new remainder 5,and apply the division lemma to get

9 = 5 x 1 + 4

We consider the new divisor 5 and the new remainder 4,and apply the division lemma to get

5 = 4 x 1 + 1

We consider the new divisor 4 and the new remainder 1,and apply the division lemma to get

4 = 1 x 4 + 0

The remainder has now become zero, so our procedure stops. Since the divisor at this stage is 1, the HCF of 73 and 908 is 1

Notice that 1 = HCF(4,1) = HCF(5,4) = HCF(9,5) = HCF(32,9) = HCF(73,32) = HCF(908,73) .

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 803, 584, 908, 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 803, 584, 908, 135?

Answer: HCF of 803, 584, 908, 135 is 1 the largest number that divides all the numbers leaving a remainder zero.

3. How to find HCF of 803, 584, 908, 135 using Euclid's Algorithm?

Answer: For arbitrary numbers 803, 584, 908, 135 apply Euclid’s Division Lemma in succession until you obtain a remainder zero. HCF is the remainder in the last but one step.