Highest Common Factor of 6664, 2149 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 6664, 2149 i.e. 7 the largest integer that leaves a remainder zero for all numbers.
HCF of 6664, 2149 is 7 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 6664, 2149 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 6664, 2149 is 7.
HCF(6664, 2149) = 7
HCF of 6664, 2149 using Euclid's algorithm
Highest common factor or Highest common divisor (hcd) can be calculated by Euclid's algotithm.
Highest common factor (HCF) of 6664, 2149 is 7.
Highest Common Factor of 6664,2149 is 7
Step 1: Since 6664 > 2149, we apply the division lemma to 6664 and 2149, to get
6664 = 2149 x 3 + 217
Step 2: Since the reminder 2149 ≠ 0, we apply division lemma to 217 and 2149, to get
2149 = 217 x 9 + 196
Step 3: We consider the new divisor 217 and the new remainder 196, and apply the division lemma to get
217 = 196 x 1 + 21
We consider the new divisor 196 and the new remainder 21,and apply the division lemma to get
196 = 21 x 9 + 7
We consider the new divisor 21 and the new remainder 7,and apply the division lemma to get
21 = 7 x 3 + 0
The remainder has now become zero, so our procedure stops. Since the divisor at this stage is 7, the HCF of 6664 and 2149 is 7
Notice that 7 = HCF(21,7) = HCF(196,21) = HCF(217,196) = HCF(2149,217) = HCF(6664,2149) .
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Frequently Asked Questions on HCF of 6664, 2149 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 6664, 2149?
Answer: HCF of 6664, 2149 is 7 the largest number that divides all the numbers leaving a remainder zero.
3. How to find HCF of 6664, 2149 using Euclid's Algorithm?
Answer: For arbitrary numbers 6664, 2149 apply Euclid’s Division Lemma in succession until you obtain a remainder zero. HCF is the remainder in the last but one step.