Highest Common Factor of 891, 192 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 891, 192 i.e. 3 the largest integer that leaves a remainder zero for all numbers.
HCF of 891, 192 is 3 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 891, 192 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 891, 192 is 3.
HCF(891, 192) = 3
HCF of 891, 192 using Euclid's algorithm
Highest common factor or Highest common divisor (hcd) can be calculated by Euclid's algotithm.
Highest common factor (HCF) of 891, 192 is 3.
Highest Common Factor of 891,192 is 3
Step 1: Since 891 > 192, we apply the division lemma to 891 and 192, to get
891 = 192 x 4 + 123
Step 2: Since the reminder 192 ≠ 0, we apply division lemma to 123 and 192, to get
192 = 123 x 1 + 69
Step 3: We consider the new divisor 123 and the new remainder 69, and apply the division lemma to get
123 = 69 x 1 + 54
We consider the new divisor 69 and the new remainder 54,and apply the division lemma to get
69 = 54 x 1 + 15
We consider the new divisor 54 and the new remainder 15,and apply the division lemma to get
54 = 15 x 3 + 9
We consider the new divisor 15 and the new remainder 9,and apply the division lemma to get
15 = 9 x 1 + 6
We consider the new divisor 9 and the new remainder 6,and apply the division lemma to get
9 = 6 x 1 + 3
We consider the new divisor 6 and the new remainder 3,and apply the division lemma to get
6 = 3 x 2 + 0
The remainder has now become zero, so our procedure stops. Since the divisor at this stage is 3, the HCF of 891 and 192 is 3
Notice that 3 = HCF(6,3) = HCF(9,6) = HCF(15,9) = HCF(54,15) = HCF(69,54) = HCF(123,69) = HCF(192,123) = HCF(891,192) .
HCF using Euclid's Algorithm Calculation Examples
Here are some samples of HCF using Euclid's Algorithm calculations.
Frequently Asked Questions on HCF of 891, 192 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 891, 192?
Answer: HCF of 891, 192 is 3 the largest number that divides all the numbers leaving a remainder zero.
3. How to find HCF of 891, 192 using Euclid's Algorithm?
Answer: For arbitrary numbers 891, 192 apply Euclid’s Division Lemma in succession until you obtain a remainder zero. HCF is the remainder in the last but one step.