Highest Common Factor of 704, 380, 376, 15 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 704, 380, 376, 15 i.e. 1 the largest integer that leaves a remainder zero for all numbers.

HCF of 704, 380, 376, 15 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 704, 380, 376, 15 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 704, 380, 376, 15 is 1.

HCF(704, 380, 376, 15) = 1

HCF of 704, 380, 376, 15 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 704, 380, 376, 15 is 1.

Highest Common Factor of 704,380,376,15 using Euclid's algorithm

Highest Common Factor of 704,380,376,15 is 1

Step 1: Since 704 > 380, we apply the division lemma to 704 and 380, to get

704 = 380 x 1 + 324

Step 2: Since the reminder 380 ≠ 0, we apply division lemma to 324 and 380, to get

380 = 324 x 1 + 56

Step 3: We consider the new divisor 324 and the new remainder 56, and apply the division lemma to get

324 = 56 x 5 + 44

We consider the new divisor 56 and the new remainder 44,and apply the division lemma to get

56 = 44 x 1 + 12

We consider the new divisor 44 and the new remainder 12,and apply the division lemma to get

44 = 12 x 3 + 8

We consider the new divisor 12 and the new remainder 8,and apply the division lemma to get

12 = 8 x 1 + 4

We consider the new divisor 8 and the new remainder 4,and apply the division lemma to get

8 = 4 x 2 + 0

The remainder has now become zero, so our procedure stops. Since the divisor at this stage is 4, the HCF of 704 and 380 is 4

Notice that 4 = HCF(8,4) = HCF(12,8) = HCF(44,12) = HCF(56,44) = HCF(324,56) = HCF(380,324) = HCF(704,380) .

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

Step 1: Since 376 > 4, we apply the division lemma to 376 and 4, to get

376 = 4 x 94 + 0

The remainder has now become zero, so our procedure stops. Since the divisor at this stage is 4, the HCF of 4 and 376 is 4

Notice that 4 = HCF(376,4) .

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

Step 1: Since 15 > 4, we apply the division lemma to 15 and 4, to get

15 = 4 x 3 + 3

Step 2: Since the reminder 4 ≠ 0, we apply division lemma to 3 and 4, to get

4 = 3 x 1 + 1

Step 3: We consider the new divisor 3 and the new remainder 1, and apply the division lemma 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 4 and 15 is 1

Notice that 1 = HCF(3,1) = HCF(4,3) = HCF(15,4) .

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Frequently Asked Questions on HCF of 704, 380, 376, 15 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 704, 380, 376, 15?

Answer: HCF of 704, 380, 376, 15 is 1 the largest number that divides all the numbers leaving a remainder zero.

3. How to find HCF of 704, 380, 376, 15 using Euclid's Algorithm?

Answer: For arbitrary numbers 704, 380, 376, 15 apply Euclid’s Division Lemma in succession until you obtain a remainder zero. HCF is the remainder in the last but one step.