Highest Common Factor of 4140, 1654 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 4140, 1654 i.e. 2 the largest integer that leaves a remainder zero for all numbers.
HCF of 4140, 1654 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 4140, 1654 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 4140, 1654 is 2.
HCF(4140, 1654) = 2
HCF of 4140, 1654 using Euclid's algorithm
Highest common factor or Highest common divisor (hcd) can be calculated by Euclid's algotithm.
Highest common factor (HCF) of 4140, 1654 is 2.
Highest Common Factor of 4140,1654 is 2
Step 1: Since 4140 > 1654, we apply the division lemma to 4140 and 1654, to get
4140 = 1654 x 2 + 832
Step 2: Since the reminder 1654 ≠ 0, we apply division lemma to 832 and 1654, to get
1654 = 832 x 1 + 822
Step 3: We consider the new divisor 832 and the new remainder 822, and apply the division lemma to get
832 = 822 x 1 + 10
We consider the new divisor 822 and the new remainder 10,and apply the division lemma to get
822 = 10 x 82 + 2
We consider the new divisor 10 and the new remainder 2,and apply the division lemma to get
10 = 2 x 5 + 0
The remainder has now become zero, so our procedure stops. Since the divisor at this stage is 2, the HCF of 4140 and 1654 is 2
Notice that 2 = HCF(10,2) = HCF(822,10) = HCF(832,822) = HCF(1654,832) = HCF(4140,1654) .
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Frequently Asked Questions on HCF of 4140, 1654 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 4140, 1654?
Answer: HCF of 4140, 1654 is 2 the largest number that divides all the numbers leaving a remainder zero.
3. How to find HCF of 4140, 1654 using Euclid's Algorithm?
Answer: For arbitrary numbers 4140, 1654 apply Euclid’s Division Lemma in succession until you obtain a remainder zero. HCF is the remainder in the last but one step.