Highest Common Factor of 7004, 546 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 7004, 546 i.e. 2 the largest integer that leaves a remainder zero for all numbers.
HCF of 7004, 546 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 7004, 546 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 7004, 546 is 2.
HCF(7004, 546) = 2
HCF of 7004, 546 using Euclid's algorithm
Highest common factor or Highest common divisor (hcd) can be calculated by Euclid's algotithm.
Highest common factor (HCF) of 7004, 546 is 2.
Highest Common Factor of 7004,546 is 2
Step 1: Since 7004 > 546, we apply the division lemma to 7004 and 546, to get
7004 = 546 x 12 + 452
Step 2: Since the reminder 546 ≠ 0, we apply division lemma to 452 and 546, to get
546 = 452 x 1 + 94
Step 3: We consider the new divisor 452 and the new remainder 94, and apply the division lemma to get
452 = 94 x 4 + 76
We consider the new divisor 94 and the new remainder 76,and apply the division lemma to get
94 = 76 x 1 + 18
We consider the new divisor 76 and the new remainder 18,and apply the division lemma to get
76 = 18 x 4 + 4
We consider the new divisor 18 and the new remainder 4,and apply the division lemma to get
18 = 4 x 4 + 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 7004 and 546 is 2
Notice that 2 = HCF(4,2) = HCF(18,4) = HCF(76,18) = HCF(94,76) = HCF(452,94) = HCF(546,452) = HCF(7004,546) .
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Frequently Asked Questions on HCF of 7004, 546 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 7004, 546?
Answer: HCF of 7004, 546 is 2 the largest number that divides all the numbers leaving a remainder zero.
3. How to find HCF of 7004, 546 using Euclid's Algorithm?
Answer: For arbitrary numbers 7004, 546 apply Euclid’s Division Lemma in succession until you obtain a remainder zero. HCF is the remainder in the last but one step.