Highest Common Factor of 768, 8898 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 768, 8898 i.e. 6 the largest integer that leaves a remainder zero for all numbers.
HCF of 768, 8898 is 6 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 768, 8898 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 768, 8898 is 6.
HCF(768, 8898) = 6
HCF of 768, 8898 using Euclid's algorithm
Highest common factor or Highest common divisor (hcd) can be calculated by Euclid's algotithm.
Highest common factor (HCF) of 768, 8898 is 6.
Highest Common Factor of 768,8898 is 6
Step 1: Since 8898 > 768, we apply the division lemma to 8898 and 768, to get
8898 = 768 x 11 + 450
Step 2: Since the reminder 768 ≠ 0, we apply division lemma to 450 and 768, to get
768 = 450 x 1 + 318
Step 3: We consider the new divisor 450 and the new remainder 318, and apply the division lemma to get
450 = 318 x 1 + 132
We consider the new divisor 318 and the new remainder 132,and apply the division lemma to get
318 = 132 x 2 + 54
We consider the new divisor 132 and the new remainder 54,and apply the division lemma to get
132 = 54 x 2 + 24
We consider the new divisor 54 and the new remainder 24,and apply the division lemma to get
54 = 24 x 2 + 6
We consider the new divisor 24 and the new remainder 6,and apply the division lemma to get
24 = 6 x 4 + 0
The remainder has now become zero, so our procedure stops. Since the divisor at this stage is 6, the HCF of 768 and 8898 is 6
Notice that 6 = HCF(24,6) = HCF(54,24) = HCF(132,54) = HCF(318,132) = HCF(450,318) = HCF(768,450) = HCF(8898,768) .
HCF using Euclid's Algorithm Calculation Examples
Here are some samples of HCF using Euclid's Algorithm calculations.
Frequently Asked Questions on HCF of 768, 8898 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 768, 8898?
Answer: HCF of 768, 8898 is 6 the largest number that divides all the numbers leaving a remainder zero.
3. How to find HCF of 768, 8898 using Euclid's Algorithm?
Answer: For arbitrary numbers 768, 8898 apply Euclid’s Division Lemma in succession until you obtain a remainder zero. HCF is the remainder in the last but one step.