Highest Common Factor of 252, 453, 978 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, 453, 978 i.e. 3 the largest integer that leaves a remainder zero for all numbers.
HCF of 252, 453, 978 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, 453, 978 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, 453, 978 is 3.
HCF(252, 453, 978) = 3
HCF of 252, 453, 978 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, 453, 978 is 3.
Highest Common Factor of 252,453,978 is 3
Step 1: Since 453 > 252, we apply the division lemma to 453 and 252, to get
453 = 252 x 1 + 201
Step 2: Since the reminder 252 ≠ 0, we apply division lemma to 201 and 252, to get
252 = 201 x 1 + 51
Step 3: We consider the new divisor 201 and the new remainder 51, and apply the division lemma to get
201 = 51 x 3 + 48
We consider the new divisor 51 and the new remainder 48,and apply the division lemma to get
51 = 48 x 1 + 3
We consider the new divisor 48 and the new remainder 3,and apply the division lemma to get
48 = 3 x 16 + 0
The remainder has now become zero, so our procedure stops. Since the divisor at this stage is 3, the HCF of 252 and 453 is 3
Notice that 3 = HCF(48,3) = HCF(51,48) = HCF(201,51) = HCF(252,201) = HCF(453,252) .
We can take hcf of as 1st numbers and next number as another number to apply in Euclidean lemma
Step 1: Since 978 > 3, we apply the division lemma to 978 and 3, to get
978 = 3 x 326 + 0
The remainder has now become zero, so our procedure stops. Since the divisor at this stage is 3, the HCF of 3 and 978 is 3
Notice that 3 = HCF(978,3) .
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, 453, 978 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, 453, 978?
Answer: HCF of 252, 453, 978 is 3 the largest number that divides all the numbers leaving a remainder zero.
3. How to find HCF of 252, 453, 978 using Euclid's Algorithm?
Answer: For arbitrary numbers 252, 453, 978 apply Euclid’s Division Lemma in succession until you obtain a remainder zero. HCF is the remainder in the last but one step.