Highest Common Factor of 360, 2514, 8465 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 360, 2514, 8465 i.e. 1 the largest integer that leaves a remainder zero for all numbers.
HCF of 360, 2514, 8465 is 1 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 360, 2514, 8465 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 360, 2514, 8465 is 1.
HCF(360, 2514, 8465) = 1
HCF of 360, 2514, 8465 using Euclid's algorithm
Highest common factor or Highest common divisor (hcd) can be calculated by Euclid's algotithm.
Highest common factor (HCF) of 360, 2514, 8465 is 1.
Highest Common Factor of 360,2514,8465 is 1
Step 1: Since 2514 > 360, we apply the division lemma to 2514 and 360, to get
2514 = 360 x 6 + 354
Step 2: Since the reminder 360 ≠ 0, we apply division lemma to 354 and 360, to get
360 = 354 x 1 + 6
Step 3: We consider the new divisor 354 and the new remainder 6, and apply the division lemma to get
354 = 6 x 59 + 0
The remainder has now become zero, so our procedure stops. Since the divisor at this stage is 6, the HCF of 360 and 2514 is 6
Notice that 6 = HCF(354,6) = HCF(360,354) = HCF(2514,360) .
We can take hcf of as 1st numbers and next number as another number to apply in Euclidean lemma
Step 1: Since 8465 > 6, we apply the division lemma to 8465 and 6, to get
8465 = 6 x 1410 + 5
Step 2: Since the reminder 6 ≠ 0, we apply division lemma to 5 and 6, to get
6 = 5 x 1 + 1
Step 3: We consider the new divisor 5 and the new remainder 1, and apply the division lemma to get
5 = 1 x 5 + 0
The remainder has now become zero, so our procedure stops. Since the divisor at this stage is 1, the HCF of 6 and 8465 is 1
Notice that 1 = HCF(5,1) = HCF(6,5) = HCF(8465,6) .
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Frequently Asked Questions on HCF of 360, 2514, 8465 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 360, 2514, 8465?
Answer: HCF of 360, 2514, 8465 is 1 the largest number that divides all the numbers leaving a remainder zero.
3. How to find HCF of 360, 2514, 8465 using Euclid's Algorithm?
Answer: For arbitrary numbers 360, 2514, 8465 apply Euclid’s Division Lemma in succession until you obtain a remainder zero. HCF is the remainder in the last but one step.