Highest Common Factor of 5004, 7954 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 5004, 7954 i.e. 2 the largest integer that leaves a remainder zero for all numbers.

HCF of 5004, 7954 is 2 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 5004, 7954 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 5004, 7954 is 2.

HCF(5004, 7954) = 2

HCF of 5004, 7954 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 5004, 7954 is 2.

Highest Common Factor of 5004,7954 using Euclid's algorithm

Highest Common Factor of 5004,7954 is 2

Step 1: Since 7954 > 5004, we apply the division lemma to 7954 and 5004, to get

7954 = 5004 x 1 + 2950

Step 2: Since the reminder 5004 ≠ 0, we apply division lemma to 2950 and 5004, to get

5004 = 2950 x 1 + 2054

Step 3: We consider the new divisor 2950 and the new remainder 2054, and apply the division lemma to get

2950 = 2054 x 1 + 896

We consider the new divisor 2054 and the new remainder 896,and apply the division lemma to get

2054 = 896 x 2 + 262

We consider the new divisor 896 and the new remainder 262,and apply the division lemma to get

896 = 262 x 3 + 110

We consider the new divisor 262 and the new remainder 110,and apply the division lemma to get

262 = 110 x 2 + 42

We consider the new divisor 110 and the new remainder 42,and apply the division lemma to get

110 = 42 x 2 + 26

We consider the new divisor 42 and the new remainder 26,and apply the division lemma to get

42 = 26 x 1 + 16

We consider the new divisor 26 and the new remainder 16,and apply the division lemma to get

26 = 16 x 1 + 10

We consider the new divisor 16 and the new remainder 10,and apply the division lemma to get

16 = 10 x 1 + 6

We consider the new divisor 10 and the new remainder 6,and apply the division lemma to get

10 = 6 x 1 + 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 5004 and 7954 is 2

Notice that 2 = HCF(4,2) = HCF(6,4) = HCF(10,6) = HCF(16,10) = HCF(26,16) = HCF(42,26) = HCF(110,42) = HCF(262,110) = HCF(896,262) = HCF(2054,896) = HCF(2950,2054) = HCF(5004,2950) = HCF(7954,5004) .

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Frequently Asked Questions on HCF of 5004, 7954 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 5004, 7954?

Answer: HCF of 5004, 7954 is 2 the largest number that divides all the numbers leaving a remainder zero.

3. How to find HCF of 5004, 7954 using Euclid's Algorithm?

Answer: For arbitrary numbers 5004, 7954 apply Euclid’s Division Lemma in succession until you obtain a remainder zero. HCF is the remainder in the last but one step.