Highest Common Factor of 3530, 2765, 65215 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 3530, 2765, 65215 i.e. 5 the largest integer that leaves a remainder zero for all numbers.
HCF of 3530, 2765, 65215 is 5 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 3530, 2765, 65215 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 3530, 2765, 65215 is 5.
HCF(3530, 2765, 65215) = 5
HCF of 3530, 2765, 65215 using Euclid's algorithm
Highest common factor or Highest common divisor (hcd) can be calculated by Euclid's algotithm.
Highest common factor (HCF) of 3530, 2765, 65215 is 5.
Highest Common Factor of 3530,2765,65215 is 5
Step 1: Since 3530 > 2765, we apply the division lemma to 3530 and 2765, to get
3530 = 2765 x 1 + 765
Step 2: Since the reminder 2765 ≠ 0, we apply division lemma to 765 and 2765, to get
2765 = 765 x 3 + 470
Step 3: We consider the new divisor 765 and the new remainder 470, and apply the division lemma to get
765 = 470 x 1 + 295
We consider the new divisor 470 and the new remainder 295,and apply the division lemma to get
470 = 295 x 1 + 175
We consider the new divisor 295 and the new remainder 175,and apply the division lemma to get
295 = 175 x 1 + 120
We consider the new divisor 175 and the new remainder 120,and apply the division lemma to get
175 = 120 x 1 + 55
We consider the new divisor 120 and the new remainder 55,and apply the division lemma to get
120 = 55 x 2 + 10
We consider the new divisor 55 and the new remainder 10,and apply the division lemma to get
55 = 10 x 5 + 5
We consider the new divisor 10 and the new remainder 5,and apply the division lemma to get
10 = 5 x 2 + 0
The remainder has now become zero, so our procedure stops. Since the divisor at this stage is 5, the HCF of 3530 and 2765 is 5
Notice that 5 = HCF(10,5) = HCF(55,10) = HCF(120,55) = HCF(175,120) = HCF(295,175) = HCF(470,295) = HCF(765,470) = HCF(2765,765) = HCF(3530,2765) .
We can take hcf of as 1st numbers and next number as another number to apply in Euclidean lemma
Step 1: Since 65215 > 5, we apply the division lemma to 65215 and 5, to get
65215 = 5 x 13043 + 0
The remainder has now become zero, so our procedure stops. Since the divisor at this stage is 5, the HCF of 5 and 65215 is 5
Notice that 5 = HCF(65215,5) .
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Frequently Asked Questions on HCF of 3530, 2765, 65215 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 3530, 2765, 65215?
Answer: HCF of 3530, 2765, 65215 is 5 the largest number that divides all the numbers leaving a remainder zero.
3. How to find HCF of 3530, 2765, 65215 using Euclid's Algorithm?
Answer: For arbitrary numbers 3530, 2765, 65215 apply Euclid’s Division Lemma in succession until you obtain a remainder zero. HCF is the remainder in the last but one step.