Highest Common Factor of 4122, 7644 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 4122, 7644 i.e. 6 the largest integer that leaves a remainder zero for all numbers.
HCF of 4122, 7644 is 6 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 4122, 7644 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 4122, 7644 is 6.
HCF(4122, 7644) = 6
HCF of 4122, 7644 using Euclid's algorithm
Highest common factor or Highest common divisor (hcd) can be calculated by Euclid's algotithm.
Highest common factor (HCF) of 4122, 7644 is 6.
Highest Common Factor of 4122,7644 is 6
Step 1: Since 7644 > 4122, we apply the division lemma to 7644 and 4122, to get
7644 = 4122 x 1 + 3522
Step 2: Since the reminder 4122 ≠ 0, we apply division lemma to 3522 and 4122, to get
4122 = 3522 x 1 + 600
Step 3: We consider the new divisor 3522 and the new remainder 600, and apply the division lemma to get
3522 = 600 x 5 + 522
We consider the new divisor 600 and the new remainder 522,and apply the division lemma to get
600 = 522 x 1 + 78
We consider the new divisor 522 and the new remainder 78,and apply the division lemma to get
522 = 78 x 6 + 54
We consider the new divisor 78 and the new remainder 54,and apply the division lemma to get
78 = 54 x 1 + 24
We consider the new divisor 54 and the new remainder 24,and apply the division lemma to get
54 = 24 x 2 + 6
We consider the new divisor 24 and the new remainder 6,and apply the division lemma to get
24 = 6 x 4 + 0
The remainder has now become zero, so our procedure stops. Since the divisor at this stage is 6, the HCF of 4122 and 7644 is 6
Notice that 6 = HCF(24,6) = HCF(54,24) = HCF(78,54) = HCF(522,78) = HCF(600,522) = HCF(3522,600) = HCF(4122,3522) = HCF(7644,4122) .
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Frequently Asked Questions on HCF of 4122, 7644 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 4122, 7644?
Answer: HCF of 4122, 7644 is 6 the largest number that divides all the numbers leaving a remainder zero.
3. How to find HCF of 4122, 7644 using Euclid's Algorithm?
Answer: For arbitrary numbers 4122, 7644 apply Euclid’s Division Lemma in succession until you obtain a remainder zero. HCF is the remainder in the last but one step.