Highest Common Factor of 407, 752, 377 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 407, 752, 377 i.e. 1 the largest integer that leaves a remainder zero for all numbers.

HCF of 407, 752, 377 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 407, 752, 377 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 407, 752, 377 is 1.

HCF(407, 752, 377) = 1

HCF of 407, 752, 377 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 407, 752, 377 is 1.

Highest Common Factor of 407,752,377 using Euclid's algorithm

Highest Common Factor of 407,752,377 is 1

Step 1: Since 752 > 407, we apply the division lemma to 752 and 407, to get

752 = 407 x 1 + 345

Step 2: Since the reminder 407 ≠ 0, we apply division lemma to 345 and 407, to get

407 = 345 x 1 + 62

Step 3: We consider the new divisor 345 and the new remainder 62, and apply the division lemma to get

345 = 62 x 5 + 35

We consider the new divisor 62 and the new remainder 35,and apply the division lemma to get

62 = 35 x 1 + 27

We consider the new divisor 35 and the new remainder 27,and apply the division lemma to get

35 = 27 x 1 + 8

We consider the new divisor 27 and the new remainder 8,and apply the division lemma to get

27 = 8 x 3 + 3

We consider the new divisor 8 and the new remainder 3,and apply the division lemma to get

8 = 3 x 2 + 2

We consider the new divisor 3 and the new remainder 2,and apply the division lemma to get

3 = 2 x 1 + 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 407 and 752 is 1

Notice that 1 = HCF(2,1) = HCF(3,2) = HCF(8,3) = HCF(27,8) = HCF(35,27) = HCF(62,35) = HCF(345,62) = HCF(407,345) = HCF(752,407) .

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

Step 1: Since 377 > 1, we apply the division lemma to 377 and 1, to get

377 = 1 x 377 + 0

The remainder has now become zero, so our procedure stops. Since the divisor at this stage is 1, the HCF of 1 and 377 is 1

Notice that 1 = HCF(377,1) .

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Frequently Asked Questions on HCF of 407, 752, 377 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 407, 752, 377?

Answer: HCF of 407, 752, 377 is 1 the largest number that divides all the numbers leaving a remainder zero.

3. How to find HCF of 407, 752, 377 using Euclid's Algorithm?

Answer: For arbitrary numbers 407, 752, 377 apply Euclid’s Division Lemma in succession until you obtain a remainder zero. HCF is the remainder in the last but one step.