Highest Common Factor of 8004, 7407 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 8004, 7407 i.e. 3 the largest integer that leaves a remainder zero for all numbers.
HCF of 8004, 7407 is 3 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 8004, 7407 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 8004, 7407 is 3.
HCF(8004, 7407) = 3
HCF of 8004, 7407 using Euclid's algorithm
Highest common factor or Highest common divisor (hcd) can be calculated by Euclid's algotithm.
Highest common factor (HCF) of 8004, 7407 is 3.
Highest Common Factor of 8004,7407 is 3
Step 1: Since 8004 > 7407, we apply the division lemma to 8004 and 7407, to get
8004 = 7407 x 1 + 597
Step 2: Since the reminder 7407 ≠ 0, we apply division lemma to 597 and 7407, to get
7407 = 597 x 12 + 243
Step 3: We consider the new divisor 597 and the new remainder 243, and apply the division lemma to get
597 = 243 x 2 + 111
We consider the new divisor 243 and the new remainder 111,and apply the division lemma to get
243 = 111 x 2 + 21
We consider the new divisor 111 and the new remainder 21,and apply the division lemma to get
111 = 21 x 5 + 6
We consider the new divisor 21 and the new remainder 6,and apply the division lemma to get
21 = 6 x 3 + 3
We consider the new divisor 6 and the new remainder 3,and apply the division lemma to get
6 = 3 x 2 + 0
The remainder has now become zero, so our procedure stops. Since the divisor at this stage is 3, the HCF of 8004 and 7407 is 3
Notice that 3 = HCF(6,3) = HCF(21,6) = HCF(111,21) = HCF(243,111) = HCF(597,243) = HCF(7407,597) = HCF(8004,7407) .
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Frequently Asked Questions on HCF of 8004, 7407 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 8004, 7407?
Answer: HCF of 8004, 7407 is 3 the largest number that divides all the numbers leaving a remainder zero.
3. How to find HCF of 8004, 7407 using Euclid's Algorithm?
Answer: For arbitrary numbers 8004, 7407 apply Euclid’s Division Lemma in succession until you obtain a remainder zero. HCF is the remainder in the last but one step.