Highest Common Factor of 648, 168 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 648, 168 i.e. 24 the largest integer that leaves a remainder zero for all numbers.
HCF of 648, 168 is 24 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 648, 168 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 648, 168 is 24.
HCF(648, 168) = 24
HCF of 648, 168 using Euclid's algorithm
Highest common factor or Highest common divisor (hcd) can be calculated by Euclid's algotithm.
Highest common factor (HCF) of 648, 168 is 24.
Highest Common Factor of 648,168 is 24
Step 1: Since 648 > 168, we apply the division lemma to 648 and 168, to get
648 = 168 x 3 + 144
Step 2: Since the reminder 168 ≠ 0, we apply division lemma to 144 and 168, to get
168 = 144 x 1 + 24
Step 3: We consider the new divisor 144 and the new remainder 24, and apply the division lemma to get
144 = 24 x 6 + 0
The remainder has now become zero, so our procedure stops. Since the divisor at this stage is 24, the HCF of 648 and 168 is 24
Notice that 24 = HCF(144,24) = HCF(168,144) = HCF(648,168) .
HCF using Euclid's Algorithm Calculation Examples
Here are some samples of HCF using Euclid's Algorithm calculations.
Frequently Asked Questions on HCF of 648, 168 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 648, 168?
Answer: HCF of 648, 168 is 24 the largest number that divides all the numbers leaving a remainder zero.
3. How to find HCF of 648, 168 using Euclid's Algorithm?
Answer: For arbitrary numbers 648, 168 apply Euclid’s Division Lemma in succession until you obtain a remainder zero. HCF is the remainder in the last but one step.