Highest Common Factor of 252, 1695 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 252, 1695 i.e. 3 the largest integer that leaves a remainder zero for all numbers.
HCF of 252, 1695 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 252, 1695 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 252, 1695 is 3.
HCF(252, 1695) = 3
HCF of 252, 1695 using Euclid's algorithm
Highest common factor or Highest common divisor (hcd) can be calculated by Euclid's algotithm.
Highest common factor (HCF) of 252, 1695 is 3.
Highest Common Factor of 252,1695 is 3
Step 1: Since 1695 > 252, we apply the division lemma to 1695 and 252, to get
1695 = 252 x 6 + 183
Step 2: Since the reminder 252 ≠ 0, we apply division lemma to 183 and 252, to get
252 = 183 x 1 + 69
Step 3: We consider the new divisor 183 and the new remainder 69, and apply the division lemma to get
183 = 69 x 2 + 45
We consider the new divisor 69 and the new remainder 45,and apply the division lemma to get
69 = 45 x 1 + 24
We consider the new divisor 45 and the new remainder 24,and apply the division lemma to get
45 = 24 x 1 + 21
We consider the new divisor 24 and the new remainder 21,and apply the division lemma to get
24 = 21 x 1 + 3
We consider the new divisor 21 and the new remainder 3,and apply the division lemma to get
21 = 3 x 7 + 0
The remainder has now become zero, so our procedure stops. Since the divisor at this stage is 3, the HCF of 252 and 1695 is 3
Notice that 3 = HCF(21,3) = HCF(24,21) = HCF(45,24) = HCF(69,45) = HCF(183,69) = HCF(252,183) = HCF(1695,252) .
HCF using Euclid's Algorithm Calculation Examples
Here are some samples of HCF using Euclid's Algorithm calculations.
Frequently Asked Questions on HCF of 252, 1695 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 252, 1695?
Answer: HCF of 252, 1695 is 3 the largest number that divides all the numbers leaving a remainder zero.
3. How to find HCF of 252, 1695 using Euclid's Algorithm?
Answer: For arbitrary numbers 252, 1695 apply Euclid’s Division Lemma in succession until you obtain a remainder zero. HCF is the remainder in the last but one step.