Highest Common Factor of 292, 8103, 1420 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 292, 8103, 1420 i.e. 1 the largest integer that leaves a remainder zero for all numbers.

HCF of 292, 8103, 1420 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 292, 8103, 1420 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 292, 8103, 1420 is 1.

HCF(292, 8103, 1420) = 1

HCF of 292, 8103, 1420 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 292, 8103, 1420 is 1.

Highest Common Factor of 292,8103,1420 using Euclid's algorithm

Highest Common Factor of 292,8103,1420 is 1

Step 1: Since 8103 > 292, we apply the division lemma to 8103 and 292, to get

8103 = 292 x 27 + 219

Step 2: Since the reminder 292 ≠ 0, we apply division lemma to 219 and 292, to get

292 = 219 x 1 + 73

Step 3: We consider the new divisor 219 and the new remainder 73, and apply the division lemma to get

219 = 73 x 3 + 0

The remainder has now become zero, so our procedure stops. Since the divisor at this stage is 73, the HCF of 292 and 8103 is 73

Notice that 73 = HCF(219,73) = HCF(292,219) = HCF(8103,292) .

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

Step 1: Since 1420 > 73, we apply the division lemma to 1420 and 73, to get

1420 = 73 x 19 + 33

Step 2: Since the reminder 73 ≠ 0, we apply division lemma to 33 and 73, to get

73 = 33 x 2 + 7

Step 3: We consider the new divisor 33 and the new remainder 7, and apply the division lemma to get

33 = 7 x 4 + 5

We consider the new divisor 7 and the new remainder 5,and apply the division lemma to get

7 = 5 x 1 + 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 73 and 1420 is 1

Notice that 1 = HCF(2,1) = HCF(5,2) = HCF(7,5) = HCF(33,7) = HCF(73,33) = HCF(1420,73) .

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Frequently Asked Questions on HCF of 292, 8103, 1420 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 292, 8103, 1420?

Answer: HCF of 292, 8103, 1420 is 1 the largest number that divides all the numbers leaving a remainder zero.

3. How to find HCF of 292, 8103, 1420 using Euclid's Algorithm?

Answer: For arbitrary numbers 292, 8103, 1420 apply Euclid’s Division Lemma in succession until you obtain a remainder zero. HCF is the remainder in the last but one step.