Highest Common Factor of 6409, 2782 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 6409, 2782 i.e. 13 the largest integer that leaves a remainder zero for all numbers.
HCF of 6409, 2782 is 13 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 6409, 2782 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 6409, 2782 is 13.
HCF(6409, 2782) = 13
HCF of 6409, 2782 using Euclid's algorithm
Highest common factor or Highest common divisor (hcd) can be calculated by Euclid's algotithm.
Highest common factor (HCF) of 6409, 2782 is 13.
Highest Common Factor of 6409,2782 is 13
Step 1: Since 6409 > 2782, we apply the division lemma to 6409 and 2782, to get
6409 = 2782 x 2 + 845
Step 2: Since the reminder 2782 ≠ 0, we apply division lemma to 845 and 2782, to get
2782 = 845 x 3 + 247
Step 3: We consider the new divisor 845 and the new remainder 247, and apply the division lemma to get
845 = 247 x 3 + 104
We consider the new divisor 247 and the new remainder 104,and apply the division lemma to get
247 = 104 x 2 + 39
We consider the new divisor 104 and the new remainder 39,and apply the division lemma to get
104 = 39 x 2 + 26
We consider the new divisor 39 and the new remainder 26,and apply the division lemma to get
39 = 26 x 1 + 13
We consider the new divisor 26 and the new remainder 13,and apply the division lemma to get
26 = 13 x 2 + 0
The remainder has now become zero, so our procedure stops. Since the divisor at this stage is 13, the HCF of 6409 and 2782 is 13
Notice that 13 = HCF(26,13) = HCF(39,26) = HCF(104,39) = HCF(247,104) = HCF(845,247) = HCF(2782,845) = HCF(6409,2782) .
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Frequently Asked Questions on HCF of 6409, 2782 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 6409, 2782?
Answer: HCF of 6409, 2782 is 13 the largest number that divides all the numbers leaving a remainder zero.
3. How to find HCF of 6409, 2782 using Euclid's Algorithm?
Answer: For arbitrary numbers 6409, 2782 apply Euclid’s Division Lemma in succession until you obtain a remainder zero. HCF is the remainder in the last but one step.