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, 5478 i.e. 6 the largest integer that leaves a remainder zero for all numbers.
HCF of 5004, 5478 is 6 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, 5478 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, 5478 is 6.
HCF(5004, 5478) = 6
Highest common factor or Highest common divisor (hcd) can be calculated by Euclid's algotithm.
Highest common factor (HCF) of 5004, 5478 is 6.
Step 1: Since 5478 > 5004, we apply the division lemma to 5478 and 5004, to get
5478 = 5004 x 1 + 474
Step 2: Since the reminder 5004 ≠ 0, we apply division lemma to 474 and 5004, to get
5004 = 474 x 10 + 264
Step 3: We consider the new divisor 474 and the new remainder 264, and apply the division lemma to get
474 = 264 x 1 + 210
We consider the new divisor 264 and the new remainder 210,and apply the division lemma to get
264 = 210 x 1 + 54
We consider the new divisor 210 and the new remainder 54,and apply the division lemma to get
210 = 54 x 3 + 48
We consider the new divisor 54 and the new remainder 48,and apply the division lemma to get
54 = 48 x 1 + 6
We consider the new divisor 48 and the new remainder 6,and apply the division lemma to get
48 = 6 x 8 + 0
The remainder has now become zero, so our procedure stops. Since the divisor at this stage is 6, the HCF of 5004 and 5478 is 6
Notice that 6 = HCF(48,6) = HCF(54,48) = HCF(210,54) = HCF(264,210) = HCF(474,264) = HCF(5004,474) = HCF(5478,5004) .
Here are some samples of HCF using Euclid's Algorithm calculations.
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, 5478?
Answer: HCF of 5004, 5478 is 6 the largest number that divides all the numbers leaving a remainder zero.
3. How to find HCF of 5004, 5478 using Euclid's Algorithm?
Answer: For arbitrary numbers 5004, 5478 apply Euclid’s Division Lemma in succession until you obtain a remainder zero. HCF is the remainder in the last but one step.