Highest Common Factor of 7504, 8430, 35919 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 7504, 8430, 35919 i.e. 1 the largest integer that leaves a remainder zero for all numbers.

HCF of 7504, 8430, 35919 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 7504, 8430, 35919 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 7504, 8430, 35919 is 1.

HCF(7504, 8430, 35919) = 1

HCF of 7504, 8430, 35919 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 7504, 8430, 35919 is 1.

Highest Common Factor of 7504,8430,35919 using Euclid's algorithm

Highest Common Factor of 7504,8430,35919 is 1

Step 1: Since 8430 > 7504, we apply the division lemma to 8430 and 7504, to get

8430 = 7504 x 1 + 926

Step 2: Since the reminder 7504 ≠ 0, we apply division lemma to 926 and 7504, to get

7504 = 926 x 8 + 96

Step 3: We consider the new divisor 926 and the new remainder 96, and apply the division lemma to get

926 = 96 x 9 + 62

We consider the new divisor 96 and the new remainder 62,and apply the division lemma to get

96 = 62 x 1 + 34

We consider the new divisor 62 and the new remainder 34,and apply the division lemma to get

62 = 34 x 1 + 28

We consider the new divisor 34 and the new remainder 28,and apply the division lemma to get

34 = 28 x 1 + 6

We consider the new divisor 28 and the new remainder 6,and apply the division lemma to get

28 = 6 x 4 + 4

We consider the new divisor 6 and the new remainder 4,and apply the division lemma to get

6 = 4 x 1 + 2

We consider the new divisor 4 and the new remainder 2,and apply the division lemma to get

4 = 2 x 2 + 0

The remainder has now become zero, so our procedure stops. Since the divisor at this stage is 2, the HCF of 7504 and 8430 is 2

Notice that 2 = HCF(4,2) = HCF(6,4) = HCF(28,6) = HCF(34,28) = HCF(62,34) = HCF(96,62) = HCF(926,96) = HCF(7504,926) = HCF(8430,7504) .

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

Step 1: Since 35919 > 2, we apply the division lemma to 35919 and 2, to get

35919 = 2 x 17959 + 1

Step 2: Since the reminder 2 ≠ 0, we apply division lemma to 1 and 2, 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 2 and 35919 is 1

Notice that 1 = HCF(2,1) = HCF(35919,2) .

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Frequently Asked Questions on HCF of 7504, 8430, 35919 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 7504, 8430, 35919?

Answer: HCF of 7504, 8430, 35919 is 1 the largest number that divides all the numbers leaving a remainder zero.

3. How to find HCF of 7504, 8430, 35919 using Euclid's Algorithm?

Answer: For arbitrary numbers 7504, 8430, 35919 apply Euclid’s Division Lemma in succession until you obtain a remainder zero. HCF is the remainder in the last but one step.