Highest Common Factor of 678, 2409 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 678, 2409 i.e. 3 the largest integer that leaves a remainder zero for all numbers.
HCF of 678, 2409 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 678, 2409 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 678, 2409 is 3.
HCF(678, 2409) = 3
HCF of 678, 2409 using Euclid's algorithm
Highest common factor or Highest common divisor (hcd) can be calculated by Euclid's algotithm.
Highest common factor (HCF) of 678, 2409 is 3.
Highest Common Factor of 678,2409 is 3
Step 1: Since 2409 > 678, we apply the division lemma to 2409 and 678, to get
2409 = 678 x 3 + 375
Step 2: Since the reminder 678 ≠ 0, we apply division lemma to 375 and 678, to get
678 = 375 x 1 + 303
Step 3: We consider the new divisor 375 and the new remainder 303, and apply the division lemma to get
375 = 303 x 1 + 72
We consider the new divisor 303 and the new remainder 72,and apply the division lemma to get
303 = 72 x 4 + 15
We consider the new divisor 72 and the new remainder 15,and apply the division lemma to get
72 = 15 x 4 + 12
We consider the new divisor 15 and the new remainder 12,and apply the division lemma to get
15 = 12 x 1 + 3
We consider the new divisor 12 and the new remainder 3,and apply the division lemma to get
12 = 3 x 4 + 0
The remainder has now become zero, so our procedure stops. Since the divisor at this stage is 3, the HCF of 678 and 2409 is 3
Notice that 3 = HCF(12,3) = HCF(15,12) = HCF(72,15) = HCF(303,72) = HCF(375,303) = HCF(678,375) = HCF(2409,678) .
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Frequently Asked Questions on HCF of 678, 2409 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 678, 2409?
Answer: HCF of 678, 2409 is 3 the largest number that divides all the numbers leaving a remainder zero.
3. How to find HCF of 678, 2409 using Euclid's Algorithm?
Answer: For arbitrary numbers 678, 2409 apply Euclid’s Division Lemma in succession until you obtain a remainder zero. HCF is the remainder in the last but one step.