Highest Common Factor of 864, 91048 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 864, 91048 i.e. 8 the largest integer that leaves a remainder zero for all numbers.
HCF of 864, 91048 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 864, 91048 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 864, 91048 is 8.
HCF(864, 91048) = 8
HCF of 864, 91048 using Euclid's algorithm
Highest common factor or Highest common divisor (hcd) can be calculated by Euclid's algotithm.
Highest common factor (HCF) of 864, 91048 is 8.
Highest Common Factor of 864,91048 is 8
Step 1: Since 91048 > 864, we apply the division lemma to 91048 and 864, to get
91048 = 864 x 105 + 328
Step 2: Since the reminder 864 ≠ 0, we apply division lemma to 328 and 864, to get
864 = 328 x 2 + 208
Step 3: We consider the new divisor 328 and the new remainder 208, and apply the division lemma to get
328 = 208 x 1 + 120
We consider the new divisor 208 and the new remainder 120,and apply the division lemma to get
208 = 120 x 1 + 88
We consider the new divisor 120 and the new remainder 88,and apply the division lemma to get
120 = 88 x 1 + 32
We consider the new divisor 88 and the new remainder 32,and apply the division lemma to get
88 = 32 x 2 + 24
We consider the new divisor 32 and the new remainder 24,and apply the division lemma to get
32 = 24 x 1 + 8
We consider the new divisor 24 and the new remainder 8,and apply the division lemma to get
24 = 8 x 3 + 0
The remainder has now become zero, so our procedure stops. Since the divisor at this stage is 8, the HCF of 864 and 91048 is 8
Notice that 8 = HCF(24,8) = HCF(32,24) = HCF(88,32) = HCF(120,88) = HCF(208,120) = HCF(328,208) = HCF(864,328) = HCF(91048,864) .
HCF using Euclid's Algorithm Calculation Examples
Here are some samples of HCF using Euclid's Algorithm calculations.
Frequently Asked Questions on HCF of 864, 91048 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 864, 91048?
Answer: HCF of 864, 91048 is 8 the largest number that divides all the numbers leaving a remainder zero.
3. How to find HCF of 864, 91048 using Euclid's Algorithm?
Answer: For arbitrary numbers 864, 91048 apply Euclid’s Division Lemma in succession until you obtain a remainder zero. HCF is the remainder in the last but one step.