Highest Common Factor of 820, 603, 105, 155 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 820, 603, 105, 155 i.e. 1 the largest integer that leaves a remainder zero for all numbers.

HCF of 820, 603, 105, 155 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 820, 603, 105, 155 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 820, 603, 105, 155 is 1.

HCF(820, 603, 105, 155) = 1

HCF of 820, 603, 105, 155 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 820, 603, 105, 155 is 1.

Highest Common Factor of 820,603,105,155 using Euclid's algorithm

Highest Common Factor of 820,603,105,155 is 1

Step 1: Since 820 > 603, we apply the division lemma to 820 and 603, to get

820 = 603 x 1 + 217

Step 2: Since the reminder 603 ≠ 0, we apply division lemma to 217 and 603, to get

603 = 217 x 2 + 169

Step 3: We consider the new divisor 217 and the new remainder 169, and apply the division lemma to get

217 = 169 x 1 + 48

We consider the new divisor 169 and the new remainder 48,and apply the division lemma to get

169 = 48 x 3 + 25

We consider the new divisor 48 and the new remainder 25,and apply the division lemma to get

48 = 25 x 1 + 23

We consider the new divisor 25 and the new remainder 23,and apply the division lemma to get

25 = 23 x 1 + 2

We consider the new divisor 23 and the new remainder 2,and apply the division lemma to get

23 = 2 x 11 + 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 820 and 603 is 1

Notice that 1 = HCF(2,1) = HCF(23,2) = HCF(25,23) = HCF(48,25) = HCF(169,48) = HCF(217,169) = HCF(603,217) = HCF(820,603) .

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

Step 1: Since 105 > 1, we apply the division lemma to 105 and 1, to get

105 = 1 x 105 + 0

The remainder has now become zero, so our procedure stops. Since the divisor at this stage is 1, the HCF of 1 and 105 is 1

Notice that 1 = HCF(105,1) .

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

Step 1: Since 155 > 1, we apply the division lemma to 155 and 1, to get

155 = 1 x 155 + 0

The remainder has now become zero, so our procedure stops. Since the divisor at this stage is 1, the HCF of 1 and 155 is 1

Notice that 1 = HCF(155,1) .

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Frequently Asked Questions on HCF of 820, 603, 105, 155 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 820, 603, 105, 155?

Answer: HCF of 820, 603, 105, 155 is 1 the largest number that divides all the numbers leaving a remainder zero.

3. How to find HCF of 820, 603, 105, 155 using Euclid's Algorithm?

Answer: For arbitrary numbers 820, 603, 105, 155 apply Euclid’s Division Lemma in succession until you obtain a remainder zero. HCF is the remainder in the last but one step.