Highest Common Factor of 6993, 9012 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 6993, 9012 i.e. 3 the largest integer that leaves a remainder zero for all numbers.
HCF of 6993, 9012 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 6993, 9012 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 6993, 9012 is 3.
HCF(6993, 9012) = 3
HCF of 6993, 9012 using Euclid's algorithm
Highest common factor or Highest common divisor (hcd) can be calculated by Euclid's algotithm.
Highest common factor (HCF) of 6993, 9012 is 3.
Highest Common Factor of 6993,9012 is 3
Step 1: Since 9012 > 6993, we apply the division lemma to 9012 and 6993, to get
9012 = 6993 x 1 + 2019
Step 2: Since the reminder 6993 ≠ 0, we apply division lemma to 2019 and 6993, to get
6993 = 2019 x 3 + 936
Step 3: We consider the new divisor 2019 and the new remainder 936, and apply the division lemma to get
2019 = 936 x 2 + 147
We consider the new divisor 936 and the new remainder 147,and apply the division lemma to get
936 = 147 x 6 + 54
We consider the new divisor 147 and the new remainder 54,and apply the division lemma to get
147 = 54 x 2 + 39
We consider the new divisor 54 and the new remainder 39,and apply the division lemma to get
54 = 39 x 1 + 15
We consider the new divisor 39 and the new remainder 15,and apply the division lemma to get
39 = 15 x 2 + 9
We consider the new divisor 15 and the new remainder 9,and apply the division lemma to get
15 = 9 x 1 + 6
We consider the new divisor 9 and the new remainder 6,and apply the division lemma to get
9 = 6 x 1 + 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 6993 and 9012 is 3
Notice that 3 = HCF(6,3) = HCF(9,6) = HCF(15,9) = HCF(39,15) = HCF(54,39) = HCF(147,54) = HCF(936,147) = HCF(2019,936) = HCF(6993,2019) = HCF(9012,6993) .
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Frequently Asked Questions on HCF of 6993, 9012 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 6993, 9012?
Answer: HCF of 6993, 9012 is 3 the largest number that divides all the numbers leaving a remainder zero.
3. How to find HCF of 6993, 9012 using Euclid's Algorithm?
Answer: For arbitrary numbers 6993, 9012 apply Euclid’s Division Lemma in succession until you obtain a remainder zero. HCF is the remainder in the last but one step.