Highest Common Factor of 374, 455 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 374, 455 i.e. 1 the largest integer that leaves a remainder zero for all numbers.

HCF of 374, 455 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 374, 455 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 374, 455 is 1.

HCF(374, 455) = 1

HCF of 374, 455 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 374, 455 is 1.

Highest Common Factor of 374,455 using Euclid's algorithm

Highest Common Factor of 374,455 is 1

Step 1: Since 455 > 374, we apply the division lemma to 455 and 374, to get

455 = 374 x 1 + 81

Step 2: Since the reminder 374 ≠ 0, we apply division lemma to 81 and 374, to get

374 = 81 x 4 + 50

Step 3: We consider the new divisor 81 and the new remainder 50, and apply the division lemma to get

81 = 50 x 1 + 31

We consider the new divisor 50 and the new remainder 31,and apply the division lemma to get

50 = 31 x 1 + 19

We consider the new divisor 31 and the new remainder 19,and apply the division lemma to get

31 = 19 x 1 + 12

We consider the new divisor 19 and the new remainder 12,and apply the division lemma to get

19 = 12 x 1 + 7

We consider the new divisor 12 and the new remainder 7,and apply the division lemma to get

12 = 7 x 1 + 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 374 and 455 is 1

Notice that 1 = HCF(2,1) = HCF(5,2) = HCF(7,5) = HCF(12,7) = HCF(19,12) = HCF(31,19) = HCF(50,31) = HCF(81,50) = HCF(374,81) = HCF(455,374) .

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Frequently Asked Questions on HCF of 374, 455 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 374, 455?

Answer: HCF of 374, 455 is 1 the largest number that divides all the numbers leaving a remainder zero.

3. How to find HCF of 374, 455 using Euclid's Algorithm?

Answer: For arbitrary numbers 374, 455 apply Euclid’s Division Lemma in succession until you obtain a remainder zero. HCF is the remainder in the last but one step.