Highest Common Factor of 2454, 1678 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 2454, 1678 i.e. 2 the largest integer that leaves a remainder zero for all numbers.
HCF of 2454, 1678 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 2454, 1678 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 2454, 1678 is 2.
HCF(2454, 1678) = 2
HCF of 2454, 1678 using Euclid's algorithm
Highest common factor or Highest common divisor (hcd) can be calculated by Euclid's algotithm.
Highest common factor (HCF) of 2454, 1678 is 2.
Highest Common Factor of 2454,1678 is 2
Step 1: Since 2454 > 1678, we apply the division lemma to 2454 and 1678, to get
2454 = 1678 x 1 + 776
Step 2: Since the reminder 1678 ≠ 0, we apply division lemma to 776 and 1678, to get
1678 = 776 x 2 + 126
Step 3: We consider the new divisor 776 and the new remainder 126, and apply the division lemma to get
776 = 126 x 6 + 20
We consider the new divisor 126 and the new remainder 20,and apply the division lemma to get
126 = 20 x 6 + 6
We consider the new divisor 20 and the new remainder 6,and apply the division lemma to get
20 = 6 x 3 + 2
We consider the new divisor 6 and the new remainder 2,and apply the division lemma to get
6 = 2 x 3 + 0
The remainder has now become zero, so our procedure stops. Since the divisor at this stage is 2, the HCF of 2454 and 1678 is 2
Notice that 2 = HCF(6,2) = HCF(20,6) = HCF(126,20) = HCF(776,126) = HCF(1678,776) = HCF(2454,1678) .
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Frequently Asked Questions on HCF of 2454, 1678 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 2454, 1678?
Answer: HCF of 2454, 1678 is 2 the largest number that divides all the numbers leaving a remainder zero.
3. How to find HCF of 2454, 1678 using Euclid's Algorithm?
Answer: For arbitrary numbers 2454, 1678 apply Euclid’s Division Lemma in succession until you obtain a remainder zero. HCF is the remainder in the last but one step.