Highest Common Factor of 368, 7514, 6460 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 368, 7514, 6460 i.e. 2 the largest integer that leaves a remainder zero for all numbers.
HCF of 368, 7514, 6460 is 2 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 368, 7514, 6460 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 368, 7514, 6460 is 2.
HCF(368, 7514, 6460) = 2
HCF of 368, 7514, 6460 using Euclid's algorithm
Highest common factor or Highest common divisor (hcd) can be calculated by Euclid's algotithm.
Highest common factor (HCF) of 368, 7514, 6460 is 2.
Highest Common Factor of 368,7514,6460 is 2
Step 1: Since 7514 > 368, we apply the division lemma to 7514 and 368, to get
7514 = 368 x 20 + 154
Step 2: Since the reminder 368 ≠ 0, we apply division lemma to 154 and 368, to get
368 = 154 x 2 + 60
Step 3: We consider the new divisor 154 and the new remainder 60, and apply the division lemma to get
154 = 60 x 2 + 34
We consider the new divisor 60 and the new remainder 34,and apply the division lemma to get
60 = 34 x 1 + 26
We consider the new divisor 34 and the new remainder 26,and apply the division lemma to get
34 = 26 x 1 + 8
We consider the new divisor 26 and the new remainder 8,and apply the division lemma to get
26 = 8 x 3 + 2
We consider the new divisor 8 and the new remainder 2,and apply the division lemma to get
8 = 2 x 4 + 0
The remainder has now become zero, so our procedure stops. Since the divisor at this stage is 2, the HCF of 368 and 7514 is 2
Notice that 2 = HCF(8,2) = HCF(26,8) = HCF(34,26) = HCF(60,34) = HCF(154,60) = HCF(368,154) = HCF(7514,368) .
We can take hcf of as 1st numbers and next number as another number to apply in Euclidean lemma
Step 1: Since 6460 > 2, we apply the division lemma to 6460 and 2, to get
6460 = 2 x 3230 + 0
The remainder has now become zero, so our procedure stops. Since the divisor at this stage is 2, the HCF of 2 and 6460 is 2
Notice that 2 = HCF(6460,2) .
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Frequently Asked Questions on HCF of 368, 7514, 6460 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 368, 7514, 6460?
Answer: HCF of 368, 7514, 6460 is 2 the largest number that divides all the numbers leaving a remainder zero.
3. How to find HCF of 368, 7514, 6460 using Euclid's Algorithm?
Answer: For arbitrary numbers 368, 7514, 6460 apply Euclid’s Division Lemma in succession until you obtain a remainder zero. HCF is the remainder in the last but one step.
