Highest Common Factor of 1654, 4640 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 1654, 4640 i.e. 2 the largest integer that leaves a remainder zero for all numbers.
HCF of 1654, 4640 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 1654, 4640 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 1654, 4640 is 2.
HCF(1654, 4640) = 2
HCF of 1654, 4640 using Euclid's algorithm
Highest common factor or Highest common divisor (hcd) can be calculated by Euclid's algotithm.
Highest common factor (HCF) of 1654, 4640 is 2.
Highest Common Factor of 1654,4640 is 2
Step 1: Since 4640 > 1654, we apply the division lemma to 4640 and 1654, to get
4640 = 1654 x 2 + 1332
Step 2: Since the reminder 1654 ≠ 0, we apply division lemma to 1332 and 1654, to get
1654 = 1332 x 1 + 322
Step 3: We consider the new divisor 1332 and the new remainder 322, and apply the division lemma to get
1332 = 322 x 4 + 44
We consider the new divisor 322 and the new remainder 44,and apply the division lemma to get
322 = 44 x 7 + 14
We consider the new divisor 44 and the new remainder 14,and apply the division lemma to get
44 = 14 x 3 + 2
We consider the new divisor 14 and the new remainder 2,and apply the division lemma to get
14 = 2 x 7 + 0
The remainder has now become zero, so our procedure stops. Since the divisor at this stage is 2, the HCF of 1654 and 4640 is 2
Notice that 2 = HCF(14,2) = HCF(44,14) = HCF(322,44) = HCF(1332,322) = HCF(1654,1332) = HCF(4640,1654) .
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Frequently Asked Questions on HCF of 1654, 4640 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 1654, 4640?
Answer: HCF of 1654, 4640 is 2 the largest number that divides all the numbers leaving a remainder zero.
3. How to find HCF of 1654, 4640 using Euclid's Algorithm?
Answer: For arbitrary numbers 1654, 4640 apply Euclid’s Division Lemma in succession until you obtain a remainder zero. HCF is the remainder in the last but one step.