Highest Common Factor of 297, 348, 370 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 297, 348, 370 i.e. 1 the largest integer that leaves a remainder zero for all numbers.

HCF of 297, 348, 370 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 297, 348, 370 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 297, 348, 370 is 1.

HCF(297, 348, 370) = 1

HCF of 297, 348, 370 using Euclid's algorithm

Highest common factor or Highest common divisor (hcd) can be calculated by Euclid's algotithm.

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Highest common factor (HCF) of 297, 348, 370 is 1.

Highest Common Factor of 297,348,370 using Euclid's algorithm

Highest Common Factor of 297,348,370 is 1

Step 1: Since 348 > 297, we apply the division lemma to 348 and 297, to get

348 = 297 x 1 + 51

Step 2: Since the reminder 297 ≠ 0, we apply division lemma to 51 and 297, to get

297 = 51 x 5 + 42

Step 3: We consider the new divisor 51 and the new remainder 42, and apply the division lemma to get

51 = 42 x 1 + 9

We consider the new divisor 42 and the new remainder 9,and apply the division lemma to get

42 = 9 x 4 + 6

We consider the new divisor 9 and the new remainder 6,and apply the division lemma to get

9 = 6 x 1 + 3

We consider the new divisor 6 and the new remainder 3,and apply the division lemma to get

6 = 3 x 2 + 0

The remainder has now become zero, so our procedure stops. Since the divisor at this stage is 3, the HCF of 297 and 348 is 3

Notice that 3 = HCF(6,3) = HCF(9,6) = HCF(42,9) = HCF(51,42) = HCF(297,51) = HCF(348,297) .

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

Step 1: Since 370 > 3, we apply the division lemma to 370 and 3, to get

370 = 3 x 123 + 1

Step 2: Since the reminder 3 ≠ 0, we apply division lemma to 1 and 3, to get

3 = 1 x 3 + 0

The remainder has now become zero, so our procedure stops. Since the divisor at this stage is 1, the HCF of 3 and 370 is 1

Notice that 1 = HCF(3,1) = HCF(370,3) .

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Frequently Asked Questions on HCF of 297, 348, 370 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 297, 348, 370?

Answer: HCF of 297, 348, 370 is 1 the largest number that divides all the numbers leaving a remainder zero.

3. How to find HCF of 297, 348, 370 using Euclid's Algorithm?

Answer: For arbitrary numbers 297, 348, 370 apply Euclid’s Division Lemma in succession until you obtain a remainder zero. HCF is the remainder in the last but one step.