Highest Common Factor of 745, 409, 400 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 745, 409, 400 i.e. 1 the largest integer that leaves a remainder zero for all numbers.

HCF of 745, 409, 400 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 745, 409, 400 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 745, 409, 400 is 1.

HCF(745, 409, 400) = 1

HCF of 745, 409, 400 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 745, 409, 400 is 1.

Highest Common Factor of 745,409,400 using Euclid's algorithm

Highest Common Factor of 745,409,400 is 1

Step 1: Since 745 > 409, we apply the division lemma to 745 and 409, to get

745 = 409 x 1 + 336

Step 2: Since the reminder 409 ≠ 0, we apply division lemma to 336 and 409, to get

409 = 336 x 1 + 73

Step 3: We consider the new divisor 336 and the new remainder 73, and apply the division lemma to get

336 = 73 x 4 + 44

We consider the new divisor 73 and the new remainder 44,and apply the division lemma to get

73 = 44 x 1 + 29

We consider the new divisor 44 and the new remainder 29,and apply the division lemma to get

44 = 29 x 1 + 15

We consider the new divisor 29 and the new remainder 15,and apply the division lemma to get

29 = 15 x 1 + 14

We consider the new divisor 15 and the new remainder 14,and apply the division lemma to get

15 = 14 x 1 + 1

We consider the new divisor 14 and the new remainder 1,and apply the division lemma to get

14 = 1 x 14 + 0

The remainder has now become zero, so our procedure stops. Since the divisor at this stage is 1, the HCF of 745 and 409 is 1

Notice that 1 = HCF(14,1) = HCF(15,14) = HCF(29,15) = HCF(44,29) = HCF(73,44) = HCF(336,73) = HCF(409,336) = HCF(745,409) .

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

Step 1: Since 400 > 1, we apply the division lemma to 400 and 1, to get

400 = 1 x 400 + 0

The remainder has now become zero, so our procedure stops. Since the divisor at this stage is 1, the HCF of 1 and 400 is 1

Notice that 1 = HCF(400,1) .

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Frequently Asked Questions on HCF of 745, 409, 400 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 745, 409, 400?

Answer: HCF of 745, 409, 400 is 1 the largest number that divides all the numbers leaving a remainder zero.

3. How to find HCF of 745, 409, 400 using Euclid's Algorithm?

Answer: For arbitrary numbers 745, 409, 400 apply Euclid’s Division Lemma in succession until you obtain a remainder zero. HCF is the remainder in the last but one step.