Highest Common Factor of 252, 921 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, 921 i.e. 3 the largest integer that leaves a remainder zero for all numbers.
HCF of 252, 921 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, 921 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, 921 is 3.
HCF(252, 921) = 3
HCF of 252, 921 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, 921 is 3.
Highest Common Factor of 252,921 is 3
Step 1: Since 921 > 252, we apply the division lemma to 921 and 252, to get
921 = 252 x 3 + 165
Step 2: Since the reminder 252 ≠ 0, we apply division lemma to 165 and 252, to get
252 = 165 x 1 + 87
Step 3: We consider the new divisor 165 and the new remainder 87, and apply the division lemma to get
165 = 87 x 1 + 78
We consider the new divisor 87 and the new remainder 78,and apply the division lemma to get
87 = 78 x 1 + 9
We consider the new divisor 78 and the new remainder 9,and apply the division lemma to get
78 = 9 x 8 + 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 252 and 921 is 3
Notice that 3 = HCF(6,3) = HCF(9,6) = HCF(78,9) = HCF(87,78) = HCF(165,87) = HCF(252,165) = HCF(921,252) .
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, 921 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, 921?
Answer: HCF of 252, 921 is 3 the largest number that divides all the numbers leaving a remainder zero.
3. How to find HCF of 252, 921 using Euclid's Algorithm?
Answer: For arbitrary numbers 252, 921 apply Euclid’s Division Lemma in succession until you obtain a remainder zero. HCF is the remainder in the last but one step.