Highest Common Factor of 64, 96, 86, 23 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 64, 96, 86, 23 i.e. 1 the largest integer that leaves a remainder zero for all numbers.
HCF of 64, 96, 86, 23 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 64, 96, 86, 23 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 64, 96, 86, 23 is 1.
HCF(64, 96, 86, 23) = 1
HCF of 64, 96, 86, 23 using Euclid's algorithm
Highest common factor or Highest common divisor (hcd) can be calculated by Euclid's algotithm.
Highest common factor (HCF) of 64, 96, 86, 23 is 1.
Highest Common Factor of 64,96,86,23 is 1
Step 1: Since 96 > 64, we apply the division lemma to 96 and 64, to get
96 = 64 x 1 + 32
Step 2: Since the reminder 64 ≠ 0, we apply division lemma to 32 and 64, to get
64 = 32 x 2 + 0
The remainder has now become zero, so our procedure stops. Since the divisor at this stage is 32, the HCF of 64 and 96 is 32
Notice that 32 = HCF(64,32) = HCF(96,64) .
We can take hcf of as 1st numbers and next number as another number to apply in Euclidean lemma
Step 1: Since 86 > 32, we apply the division lemma to 86 and 32, to get
86 = 32 x 2 + 22
Step 2: Since the reminder 32 ≠ 0, we apply division lemma to 22 and 32, to get
32 = 22 x 1 + 10
Step 3: 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 32 and 86 is 2
Notice that 2 = HCF(10,2) = HCF(22,10) = HCF(32,22) = HCF(86,32) .
We can take hcf of as 1st numbers and next number as another number to apply in Euclidean lemma
Step 1: Since 23 > 2, we apply the division lemma to 23 and 2, to get
23 = 2 x 11 + 1
Step 2: Since the reminder 2 ≠ 0, we apply division lemma to 1 and 2, to get
2 = 1 x 2 + 0
The remainder has now become zero, so our procedure stops. Since the divisor at this stage is 1, the HCF of 2 and 23 is 1
Notice that 1 = HCF(2,1) = HCF(23,2) .
HCF using Euclid's Algorithm Calculation Examples
Here are some samples of HCF using Euclid's Algorithm calculations.
Frequently Asked Questions on HCF of 64, 96, 86, 23 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 64, 96, 86, 23?
Answer: HCF of 64, 96, 86, 23 is 1 the largest number that divides all the numbers leaving a remainder zero.
3. How to find HCF of 64, 96, 86, 23 using Euclid's Algorithm?
Answer: For arbitrary numbers 64, 96, 86, 23 apply Euclid’s Division Lemma in succession until you obtain a remainder zero. HCF is the remainder in the last but one step.