Highest Common Factor of 162, 864, 305 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 162, 864, 305 i.e. 1 the largest integer that leaves a remainder zero for all numbers.
HCF of 162, 864, 305 is 1 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 162, 864, 305 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 162, 864, 305 is 1.
HCF(162, 864, 305) = 1
HCF of 162, 864, 305 using Euclid's algorithm
Highest common factor or Highest common divisor (hcd) can be calculated by Euclid's algotithm.
Highest common factor (HCF) of 162, 864, 305 is 1.
Highest Common Factor of 162,864,305 is 1
Step 1: Since 864 > 162, we apply the division lemma to 864 and 162, to get
864 = 162 x 5 + 54
Step 2: Since the reminder 162 ≠ 0, we apply division lemma to 54 and 162, to get
162 = 54 x 3 + 0
The remainder has now become zero, so our procedure stops. Since the divisor at this stage is 54, the HCF of 162 and 864 is 54
Notice that 54 = HCF(162,54) = HCF(864,162) .
We can take hcf of as 1st numbers and next number as another number to apply in Euclidean lemma
Step 1: Since 305 > 54, we apply the division lemma to 305 and 54, to get
305 = 54 x 5 + 35
Step 2: Since the reminder 54 ≠ 0, we apply division lemma to 35 and 54, to get
54 = 35 x 1 + 19
Step 3: We consider the new divisor 35 and the new remainder 19, and apply the division lemma to get
35 = 19 x 1 + 16
We consider the new divisor 19 and the new remainder 16,and apply the division lemma to get
19 = 16 x 1 + 3
We consider the new divisor 16 and the new remainder 3,and apply the division lemma to get
16 = 3 x 5 + 1
We consider the new divisor 3 and the new remainder 1,and apply the division lemma to get
3 = 1 x 3 + 0
The remainder has now become zero, so our procedure stops. Since the divisor at this stage is 1, the HCF of 54 and 305 is 1
Notice that 1 = HCF(3,1) = HCF(16,3) = HCF(19,16) = HCF(35,19) = HCF(54,35) = HCF(305,54) .
HCF using Euclid's Algorithm Calculation Examples
Here are some samples of HCF using Euclid's Algorithm calculations.
Frequently Asked Questions on HCF of 162, 864, 305 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 162, 864, 305?
Answer: HCF of 162, 864, 305 is 1 the largest number that divides all the numbers leaving a remainder zero.
3. How to find HCF of 162, 864, 305 using Euclid's Algorithm?
Answer: For arbitrary numbers 162, 864, 305 apply Euclid’s Division Lemma in succession until you obtain a remainder zero. HCF is the remainder in the last but one step.