Highest Common Factor of 614, 1648 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 614, 1648 i.e. 2 the largest integer that leaves a remainder zero for all numbers.
HCF of 614, 1648 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 614, 1648 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 614, 1648 is 2.
HCF(614, 1648) = 2
HCF of 614, 1648 using Euclid's algorithm
Highest common factor or Highest common divisor (hcd) can be calculated by Euclid's algotithm.
Highest common factor (HCF) of 614, 1648 is 2.
Highest Common Factor of 614,1648 is 2
Step 1: Since 1648 > 614, we apply the division lemma to 1648 and 614, to get
1648 = 614 x 2 + 420
Step 2: Since the reminder 614 ≠ 0, we apply division lemma to 420 and 614, to get
614 = 420 x 1 + 194
Step 3: We consider the new divisor 420 and the new remainder 194, and apply the division lemma to get
420 = 194 x 2 + 32
We consider the new divisor 194 and the new remainder 32,and apply the division lemma to get
194 = 32 x 6 + 2
We consider the new divisor 32 and the new remainder 2,and apply the division lemma to get
32 = 2 x 16 + 0
The remainder has now become zero, so our procedure stops. Since the divisor at this stage is 2, the HCF of 614 and 1648 is 2
Notice that 2 = HCF(32,2) = HCF(194,32) = HCF(420,194) = HCF(614,420) = HCF(1648,614) .
HCF using Euclid's Algorithm Calculation Examples
Here are some samples of HCF using Euclid's Algorithm calculations.
Frequently Asked Questions on HCF of 614, 1648 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 614, 1648?
Answer: HCF of 614, 1648 is 2 the largest number that divides all the numbers leaving a remainder zero.
3. How to find HCF of 614, 1648 using Euclid's Algorithm?
Answer: For arbitrary numbers 614, 1648 apply Euclid’s Division Lemma in succession until you obtain a remainder zero. HCF is the remainder in the last but one step.