Highest Common Factor of 218, 1609 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 218, 1609 i.e. 1 the largest integer that leaves a remainder zero for all numbers.
HCF of 218, 1609 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 218, 1609 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 218, 1609 is 1.
HCF(218, 1609) = 1
HCF of 218, 1609 using Euclid's algorithm
Highest common factor or Highest common divisor (hcd) can be calculated by Euclid's algotithm.
Highest common factor (HCF) of 218, 1609 is 1.
Highest Common Factor of 218,1609 is 1
Step 1: Since 1609 > 218, we apply the division lemma to 1609 and 218, to get
1609 = 218 x 7 + 83
Step 2: Since the reminder 218 ≠ 0, we apply division lemma to 83 and 218, to get
218 = 83 x 2 + 52
Step 3: We consider the new divisor 83 and the new remainder 52, and apply the division lemma to get
83 = 52 x 1 + 31
We consider the new divisor 52 and the new remainder 31,and apply the division lemma to get
52 = 31 x 1 + 21
We consider the new divisor 31 and the new remainder 21,and apply the division lemma to get
31 = 21 x 1 + 10
We consider the new divisor 21 and the new remainder 10,and apply the division lemma to get
21 = 10 x 2 + 1
We consider the new divisor 10 and the new remainder 1,and apply the division lemma to get
10 = 1 x 10 + 0
The remainder has now become zero, so our procedure stops. Since the divisor at this stage is 1, the HCF of 218 and 1609 is 1
Notice that 1 = HCF(10,1) = HCF(21,10) = HCF(31,21) = HCF(52,31) = HCF(83,52) = HCF(218,83) = HCF(1609,218) .
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Frequently Asked Questions on HCF of 218, 1609 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 218, 1609?
Answer: HCF of 218, 1609 is 1 the largest number that divides all the numbers leaving a remainder zero.
3. How to find HCF of 218, 1609 using Euclid's Algorithm?
Answer: For arbitrary numbers 218, 1609 apply Euclid’s Division Lemma in succession until you obtain a remainder zero. HCF is the remainder in the last but one step.