Highest Common Factor of 459, 2208 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 459, 2208 i.e. 3 the largest integer that leaves a remainder zero for all numbers.
HCF of 459, 2208 is 3 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 459, 2208 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 459, 2208 is 3.
HCF(459, 2208) = 3
HCF of 459, 2208 using Euclid's algorithm
Highest common factor or Highest common divisor (hcd) can be calculated by Euclid's algotithm.
Highest common factor (HCF) of 459, 2208 is 3.
Highest Common Factor of 459,2208 is 3
Step 1: Since 2208 > 459, we apply the division lemma to 2208 and 459, to get
2208 = 459 x 4 + 372
Step 2: Since the reminder 459 ≠ 0, we apply division lemma to 372 and 459, to get
459 = 372 x 1 + 87
Step 3: We consider the new divisor 372 and the new remainder 87, and apply the division lemma to get
372 = 87 x 4 + 24
We consider the new divisor 87 and the new remainder 24,and apply the division lemma to get
87 = 24 x 3 + 15
We consider the new divisor 24 and the new remainder 15,and apply the division lemma to get
24 = 15 x 1 + 9
We consider the new divisor 15 and the new remainder 9,and apply the division lemma to get
15 = 9 x 1 + 6
We consider the new divisor 9 and the new remainder 6,and apply the division lemma to get
9 = 6 x 1 + 3
We consider the new divisor 6 and the new remainder 3,and apply the division lemma to get
6 = 3 x 2 + 0
The remainder has now become zero, so our procedure stops. Since the divisor at this stage is 3, the HCF of 459 and 2208 is 3
Notice that 3 = HCF(6,3) = HCF(9,6) = HCF(15,9) = HCF(24,15) = HCF(87,24) = HCF(372,87) = HCF(459,372) = HCF(2208,459) .
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Frequently Asked Questions on HCF of 459, 2208 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 459, 2208?
Answer: HCF of 459, 2208 is 3 the largest number that divides all the numbers leaving a remainder zero.
3. How to find HCF of 459, 2208 using Euclid's Algorithm?
Answer: For arbitrary numbers 459, 2208 apply Euclid’s Division Lemma in succession until you obtain a remainder zero. HCF is the remainder in the last but one step.