Highest Common Factor of 3004, 9648 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 3004, 9648 i.e. 4 the largest integer that leaves a remainder zero for all numbers.
HCF of 3004, 9648 is 4 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 3004, 9648 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 3004, 9648 is 4.
HCF(3004, 9648) = 4
HCF of 3004, 9648 using Euclid's algorithm
Highest common factor or Highest common divisor (hcd) can be calculated by Euclid's algotithm.
Highest common factor (HCF) of 3004, 9648 is 4.
Highest Common Factor of 3004,9648 is 4
Step 1: Since 9648 > 3004, we apply the division lemma to 9648 and 3004, to get
9648 = 3004 x 3 + 636
Step 2: Since the reminder 3004 ≠ 0, we apply division lemma to 636 and 3004, to get
3004 = 636 x 4 + 460
Step 3: We consider the new divisor 636 and the new remainder 460, and apply the division lemma to get
636 = 460 x 1 + 176
We consider the new divisor 460 and the new remainder 176,and apply the division lemma to get
460 = 176 x 2 + 108
We consider the new divisor 176 and the new remainder 108,and apply the division lemma to get
176 = 108 x 1 + 68
We consider the new divisor 108 and the new remainder 68,and apply the division lemma to get
108 = 68 x 1 + 40
We consider the new divisor 68 and the new remainder 40,and apply the division lemma to get
68 = 40 x 1 + 28
We consider the new divisor 40 and the new remainder 28,and apply the division lemma to get
40 = 28 x 1 + 12
We consider the new divisor 28 and the new remainder 12,and apply the division lemma to get
28 = 12 x 2 + 4
We consider the new divisor 12 and the new remainder 4,and apply the division lemma to get
12 = 4 x 3 + 0
The remainder has now become zero, so our procedure stops. Since the divisor at this stage is 4, the HCF of 3004 and 9648 is 4
Notice that 4 = HCF(12,4) = HCF(28,12) = HCF(40,28) = HCF(68,40) = HCF(108,68) = HCF(176,108) = HCF(460,176) = HCF(636,460) = HCF(3004,636) = HCF(9648,3004) .
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Frequently Asked Questions on HCF of 3004, 9648 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 3004, 9648?
Answer: HCF of 3004, 9648 is 4 the largest number that divides all the numbers leaving a remainder zero.
3. How to find HCF of 3004, 9648 using Euclid's Algorithm?
Answer: For arbitrary numbers 3004, 9648 apply Euclid’s Division Lemma in succession until you obtain a remainder zero. HCF is the remainder in the last but one step.