Highest Common Factor of 6003, 6897 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 6003, 6897 i.e. 3 the largest integer that leaves a remainder zero for all numbers.
HCF of 6003, 6897 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 6003, 6897 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 6003, 6897 is 3.
HCF(6003, 6897) = 3
HCF of 6003, 6897 using Euclid's algorithm
Highest common factor or Highest common divisor (hcd) can be calculated by Euclid's algotithm.
Highest common factor (HCF) of 6003, 6897 is 3.
Highest Common Factor of 6003,6897 is 3
Step 1: Since 6897 > 6003, we apply the division lemma to 6897 and 6003, to get
6897 = 6003 x 1 + 894
Step 2: Since the reminder 6003 ≠ 0, we apply division lemma to 894 and 6003, to get
6003 = 894 x 6 + 639
Step 3: We consider the new divisor 894 and the new remainder 639, and apply the division lemma to get
894 = 639 x 1 + 255
We consider the new divisor 639 and the new remainder 255,and apply the division lemma to get
639 = 255 x 2 + 129
We consider the new divisor 255 and the new remainder 129,and apply the division lemma to get
255 = 129 x 1 + 126
We consider the new divisor 129 and the new remainder 126,and apply the division lemma to get
129 = 126 x 1 + 3
We consider the new divisor 126 and the new remainder 3,and apply the division lemma to get
126 = 3 x 42 + 0
The remainder has now become zero, so our procedure stops. Since the divisor at this stage is 3, the HCF of 6003 and 6897 is 3
Notice that 3 = HCF(126,3) = HCF(129,126) = HCF(255,129) = HCF(639,255) = HCF(894,639) = HCF(6003,894) = HCF(6897,6003) .
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Frequently Asked Questions on HCF of 6003, 6897 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 6003, 6897?
Answer: HCF of 6003, 6897 is 3 the largest number that divides all the numbers leaving a remainder zero.
3. How to find HCF of 6003, 6897 using Euclid's Algorithm?
Answer: For arbitrary numbers 6003, 6897 apply Euclid’s Division Lemma in succession until you obtain a remainder zero. HCF is the remainder in the last but one step.