Highest Common Factor of 330, 6105, 7428 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 330, 6105, 7428 i.e. 3 the largest integer that leaves a remainder zero for all numbers.
HCF of 330, 6105, 7428 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 330, 6105, 7428 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 330, 6105, 7428 is 3.
HCF(330, 6105, 7428) = 3
HCF of 330, 6105, 7428 using Euclid's algorithm
Highest common factor or Highest common divisor (hcd) can be calculated by Euclid's algotithm.
Highest common factor (HCF) of 330, 6105, 7428 is 3.
Highest Common Factor of 330,6105,7428 is 3
Step 1: Since 6105 > 330, we apply the division lemma to 6105 and 330, to get
6105 = 330 x 18 + 165
Step 2: Since the reminder 330 ≠ 0, we apply division lemma to 165 and 330, to get
330 = 165 x 2 + 0
The remainder has now become zero, so our procedure stops. Since the divisor at this stage is 165, the HCF of 330 and 6105 is 165
Notice that 165 = HCF(330,165) = HCF(6105,330) .
We can take hcf of as 1st numbers and next number as another number to apply in Euclidean lemma
Step 1: Since 7428 > 165, we apply the division lemma to 7428 and 165, to get
7428 = 165 x 45 + 3
Step 2: Since the reminder 165 ≠ 0, we apply division lemma to 3 and 165, to get
165 = 3 x 55 + 0
The remainder has now become zero, so our procedure stops. Since the divisor at this stage is 3, the HCF of 165 and 7428 is 3
Notice that 3 = HCF(165,3) = HCF(7428,165) .
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Frequently Asked Questions on HCF of 330, 6105, 7428 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 330, 6105, 7428?
Answer: HCF of 330, 6105, 7428 is 3 the largest number that divides all the numbers leaving a remainder zero.
3. How to find HCF of 330, 6105, 7428 using Euclid's Algorithm?
Answer: For arbitrary numbers 330, 6105, 7428 apply Euclid’s Division Lemma in succession until you obtain a remainder zero. HCF is the remainder in the last but one step.