Highest Common Factor of 6345, 4074 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 6345, 4074 i.e. 3 the largest integer that leaves a remainder zero for all numbers.
HCF of 6345, 4074 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 6345, 4074 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 6345, 4074 is 3.
HCF(6345, 4074) = 3
HCF of 6345, 4074 using Euclid's algorithm
Highest common factor or Highest common divisor (hcd) can be calculated by Euclid's algotithm.
Highest common factor (HCF) of 6345, 4074 is 3.
Highest Common Factor of 6345,4074 is 3
Step 1: Since 6345 > 4074, we apply the division lemma to 6345 and 4074, to get
6345 = 4074 x 1 + 2271
Step 2: Since the reminder 4074 ≠ 0, we apply division lemma to 2271 and 4074, to get
4074 = 2271 x 1 + 1803
Step 3: We consider the new divisor 2271 and the new remainder 1803, and apply the division lemma to get
2271 = 1803 x 1 + 468
We consider the new divisor 1803 and the new remainder 468,and apply the division lemma to get
1803 = 468 x 3 + 399
We consider the new divisor 468 and the new remainder 399,and apply the division lemma to get
468 = 399 x 1 + 69
We consider the new divisor 399 and the new remainder 69,and apply the division lemma to get
399 = 69 x 5 + 54
We consider the new divisor 69 and the new remainder 54,and apply the division lemma to get
69 = 54 x 1 + 15
We consider the new divisor 54 and the new remainder 15,and apply the division lemma to get
54 = 15 x 3 + 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 6345 and 4074 is 3
Notice that 3 = HCF(6,3) = HCF(9,6) = HCF(15,9) = HCF(54,15) = HCF(69,54) = HCF(399,69) = HCF(468,399) = HCF(1803,468) = HCF(2271,1803) = HCF(4074,2271) = HCF(6345,4074) .
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Frequently Asked Questions on HCF of 6345, 4074 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 6345, 4074?
Answer: HCF of 6345, 4074 is 3 the largest number that divides all the numbers leaving a remainder zero.
3. How to find HCF of 6345, 4074 using Euclid's Algorithm?
Answer: For arbitrary numbers 6345, 4074 apply Euclid’s Division Lemma in succession until you obtain a remainder zero. HCF is the remainder in the last but one step.