Highest Common Factor of 3516, 5414 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 3516, 5414 i.e. 2 the largest integer that leaves a remainder zero for all numbers.
HCF of 3516, 5414 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 3516, 5414 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 3516, 5414 is 2.
HCF(3516, 5414) = 2
HCF of 3516, 5414 using Euclid's algorithm
Highest common factor or Highest common divisor (hcd) can be calculated by Euclid's algotithm.
Highest common factor (HCF) of 3516, 5414 is 2.
Highest Common Factor of 3516,5414 is 2
Step 1: Since 5414 > 3516, we apply the division lemma to 5414 and 3516, to get
5414 = 3516 x 1 + 1898
Step 2: Since the reminder 3516 ≠ 0, we apply division lemma to 1898 and 3516, to get
3516 = 1898 x 1 + 1618
Step 3: We consider the new divisor 1898 and the new remainder 1618, and apply the division lemma to get
1898 = 1618 x 1 + 280
We consider the new divisor 1618 and the new remainder 280,and apply the division lemma to get
1618 = 280 x 5 + 218
We consider the new divisor 280 and the new remainder 218,and apply the division lemma to get
280 = 218 x 1 + 62
We consider the new divisor 218 and the new remainder 62,and apply the division lemma to get
218 = 62 x 3 + 32
We consider the new divisor 62 and the new remainder 32,and apply the division lemma to get
62 = 32 x 1 + 30
We consider the new divisor 32 and the new remainder 30,and apply the division lemma to get
32 = 30 x 1 + 2
We consider the new divisor 30 and the new remainder 2,and apply the division lemma to get
30 = 2 x 15 + 0
The remainder has now become zero, so our procedure stops. Since the divisor at this stage is 2, the HCF of 3516 and 5414 is 2
Notice that 2 = HCF(30,2) = HCF(32,30) = HCF(62,32) = HCF(218,62) = HCF(280,218) = HCF(1618,280) = HCF(1898,1618) = HCF(3516,1898) = HCF(5414,3516) .
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Frequently Asked Questions on HCF of 3516, 5414 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 3516, 5414?
Answer: HCF of 3516, 5414 is 2 the largest number that divides all the numbers leaving a remainder zero.
3. How to find HCF of 3516, 5414 using Euclid's Algorithm?
Answer: For arbitrary numbers 3516, 5414 apply Euclid’s Division Lemma in succession until you obtain a remainder zero. HCF is the remainder in the last but one step.