Highest Common Factor of 6741, 4374 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 6741, 4374 i.e. 9 the largest integer that leaves a remainder zero for all numbers.
HCF of 6741, 4374 is 9 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 6741, 4374 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 6741, 4374 is 9.
HCF(6741, 4374) = 9
HCF of 6741, 4374 using Euclid's algorithm
Highest common factor or Highest common divisor (hcd) can be calculated by Euclid's algotithm.
Highest common factor (HCF) of 6741, 4374 is 9.
Highest Common Factor of 6741,4374 is 9
Step 1: Since 6741 > 4374, we apply the division lemma to 6741 and 4374, to get
6741 = 4374 x 1 + 2367
Step 2: Since the reminder 4374 ≠ 0, we apply division lemma to 2367 and 4374, to get
4374 = 2367 x 1 + 2007
Step 3: We consider the new divisor 2367 and the new remainder 2007, and apply the division lemma to get
2367 = 2007 x 1 + 360
We consider the new divisor 2007 and the new remainder 360,and apply the division lemma to get
2007 = 360 x 5 + 207
We consider the new divisor 360 and the new remainder 207,and apply the division lemma to get
360 = 207 x 1 + 153
We consider the new divisor 207 and the new remainder 153,and apply the division lemma to get
207 = 153 x 1 + 54
We consider the new divisor 153 and the new remainder 54,and apply the division lemma to get
153 = 54 x 2 + 45
We consider the new divisor 54 and the new remainder 45,and apply the division lemma to get
54 = 45 x 1 + 9
We consider the new divisor 45 and the new remainder 9,and apply the division lemma to get
45 = 9 x 5 + 0
The remainder has now become zero, so our procedure stops. Since the divisor at this stage is 9, the HCF of 6741 and 4374 is 9
Notice that 9 = HCF(45,9) = HCF(54,45) = HCF(153,54) = HCF(207,153) = HCF(360,207) = HCF(2007,360) = HCF(2367,2007) = HCF(4374,2367) = HCF(6741,4374) .
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Frequently Asked Questions on HCF of 6741, 4374 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 6741, 4374?
Answer: HCF of 6741, 4374 is 9 the largest number that divides all the numbers leaving a remainder zero.
3. How to find HCF of 6741, 4374 using Euclid's Algorithm?
Answer: For arbitrary numbers 6741, 4374 apply Euclid’s Division Lemma in succession until you obtain a remainder zero. HCF is the remainder in the last but one step.
