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, 8454 i.e. 2 the largest integer that leaves a remainder zero for all numbers.
HCF of 824, 8454 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 824, 8454 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, 8454 is 2.
HCF(824, 8454) = 2
Highest common factor or Highest common divisor (hcd) can be calculated by Euclid's algotithm.
Highest common factor (HCF) of 824, 8454 is 2.
Step 1: Since 8454 > 824, we apply the division lemma to 8454 and 824, to get
8454 = 824 x 10 + 214
Step 2: Since the reminder 824 ≠ 0, we apply division lemma to 214 and 824, to get
824 = 214 x 3 + 182
Step 3: We consider the new divisor 214 and the new remainder 182, and apply the division lemma to get
214 = 182 x 1 + 32
We consider the new divisor 182 and the new remainder 32,and apply the division lemma to get
182 = 32 x 5 + 22
We consider the new divisor 32 and the new remainder 22,and apply the division lemma to get
32 = 22 x 1 + 10
We consider the new divisor 22 and the new remainder 10,and apply the division lemma to get
22 = 10 x 2 + 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 824 and 8454 is 2
Notice that 2 = HCF(10,2) = HCF(22,10) = HCF(32,22) = HCF(182,32) = HCF(214,182) = HCF(824,214) = HCF(8454,824) .
Here are some samples of HCF using Euclid's Algorithm calculations.
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, 8454?
Answer: HCF of 824, 8454 is 2 the largest number that divides all the numbers leaving a remainder zero.
3. How to find HCF of 824, 8454 using Euclid's Algorithm?
Answer: For arbitrary numbers 824, 8454 apply Euclid’s Division Lemma in succession until you obtain a remainder zero. HCF is the remainder in the last but one step.