Highest Common Factor of 902, 349, 448 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 902, 349, 448 i.e. 1 the largest integer that leaves a remainder zero for all numbers.

HCF of 902, 349, 448 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 902, 349, 448 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 902, 349, 448 is 1.

HCF(902, 349, 448) = 1

HCF of 902, 349, 448 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 902, 349, 448 is 1.

Highest Common Factor of 902,349,448 using Euclid's algorithm

Highest Common Factor of 902,349,448 is 1

Step 1: Since 902 > 349, we apply the division lemma to 902 and 349, to get

902 = 349 x 2 + 204

Step 2: Since the reminder 349 ≠ 0, we apply division lemma to 204 and 349, to get

349 = 204 x 1 + 145

Step 3: We consider the new divisor 204 and the new remainder 145, and apply the division lemma to get

204 = 145 x 1 + 59

We consider the new divisor 145 and the new remainder 59,and apply the division lemma to get

145 = 59 x 2 + 27

We consider the new divisor 59 and the new remainder 27,and apply the division lemma to get

59 = 27 x 2 + 5

We consider the new divisor 27 and the new remainder 5,and apply the division lemma to get

27 = 5 x 5 + 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 902 and 349 is 1

Notice that 1 = HCF(2,1) = HCF(5,2) = HCF(27,5) = HCF(59,27) = HCF(145,59) = HCF(204,145) = HCF(349,204) = HCF(902,349) .

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

Step 1: Since 448 > 1, we apply the division lemma to 448 and 1, to get

448 = 1 x 448 + 0

The remainder has now become zero, so our procedure stops. Since the divisor at this stage is 1, the HCF of 1 and 448 is 1

Notice that 1 = HCF(448,1) .

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Frequently Asked Questions on HCF of 902, 349, 448 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 902, 349, 448?

Answer: HCF of 902, 349, 448 is 1 the largest number that divides all the numbers leaving a remainder zero.

3. How to find HCF of 902, 349, 448 using Euclid's Algorithm?

Answer: For arbitrary numbers 902, 349, 448 apply Euclid’s Division Lemma in succession until you obtain a remainder zero. HCF is the remainder in the last but one step.