Highest Common Factor of 824, 648 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 824, 648 i.e. 8 the largest integer that leaves a remainder zero for all numbers.
HCF of 824, 648 is 8 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 824, 648 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 824, 648 is 8.
HCF(824, 648) = 8
HCF of 824, 648 using Euclid's algorithm
Highest common factor or Highest common divisor (hcd) can be calculated by Euclid's algotithm.
Highest common factor (HCF) of 824, 648 is 8.
Highest Common Factor of 824,648 is 8
Step 1: Since 824 > 648, we apply the division lemma to 824 and 648, to get
824 = 648 x 1 + 176
Step 2: Since the reminder 648 ≠ 0, we apply division lemma to 176 and 648, to get
648 = 176 x 3 + 120
Step 3: We consider the new divisor 176 and the new remainder 120, and apply the division lemma to get
176 = 120 x 1 + 56
We consider the new divisor 120 and the new remainder 56,and apply the division lemma to get
120 = 56 x 2 + 8
We consider the new divisor 56 and the new remainder 8,and apply the division lemma to get
56 = 8 x 7 + 0
The remainder has now become zero, so our procedure stops. Since the divisor at this stage is 8, the HCF of 824 and 648 is 8
Notice that 8 = HCF(56,8) = HCF(120,56) = HCF(176,120) = HCF(648,176) = HCF(824,648) .
HCF using Euclid's Algorithm Calculation Examples
Here are some samples of HCF using Euclid's Algorithm calculations.
Frequently Asked Questions on HCF of 824, 648 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 824, 648?
Answer: HCF of 824, 648 is 8 the largest number that divides all the numbers leaving a remainder zero.
3. How to find HCF of 824, 648 using Euclid's Algorithm?
Answer: For arbitrary numbers 824, 648 apply Euclid’s Division Lemma in succession until you obtain a remainder zero. HCF is the remainder in the last but one step.