Highest Common Factor of 665, 852 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 665, 852 i.e. 1 the largest integer that leaves a remainder zero for all numbers.
HCF of 665, 852 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 665, 852 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 665, 852 is 1.
HCF(665, 852) = 1
HCF of 665, 852 using Euclid's algorithm
Highest common factor or Highest common divisor (hcd) can be calculated by Euclid's algotithm.
Highest common factor (HCF) of 665, 852 is 1.
Highest Common Factor of 665,852 is 1
Step 1: Since 852 > 665, we apply the division lemma to 852 and 665, to get
852 = 665 x 1 + 187
Step 2: Since the reminder 665 ≠ 0, we apply division lemma to 187 and 665, to get
665 = 187 x 3 + 104
Step 3: We consider the new divisor 187 and the new remainder 104, and apply the division lemma to get
187 = 104 x 1 + 83
We consider the new divisor 104 and the new remainder 83,and apply the division lemma to get
104 = 83 x 1 + 21
We consider the new divisor 83 and the new remainder 21,and apply the division lemma to get
83 = 21 x 3 + 20
We consider the new divisor 21 and the new remainder 20,and apply the division lemma to get
21 = 20 x 1 + 1
We consider the new divisor 20 and the new remainder 1,and apply the division lemma to get
20 = 1 x 20 + 0
The remainder has now become zero, so our procedure stops. Since the divisor at this stage is 1, the HCF of 665 and 852 is 1
Notice that 1 = HCF(20,1) = HCF(21,20) = HCF(83,21) = HCF(104,83) = HCF(187,104) = HCF(665,187) = HCF(852,665) .
HCF using Euclid's Algorithm Calculation Examples
Here are some samples of HCF using Euclid's Algorithm calculations.
Frequently Asked Questions on HCF of 665, 852 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 665, 852?
Answer: HCF of 665, 852 is 1 the largest number that divides all the numbers leaving a remainder zero.
3. How to find HCF of 665, 852 using Euclid's Algorithm?
Answer: For arbitrary numbers 665, 852 apply Euclid’s Division Lemma in succession until you obtain a remainder zero. HCF is the remainder in the last but one step.