Highest Common Factor of 378, 199, 225 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 378, 199, 225 i.e. 1 the largest integer that leaves a remainder zero for all numbers.
HCF of 378, 199, 225 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 378, 199, 225 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 378, 199, 225 is 1.
HCF(378, 199, 225) = 1
HCF of 378, 199, 225 using Euclid's algorithm
Highest common factor or Highest common divisor (hcd) can be calculated by Euclid's algotithm.
Highest common factor (HCF) of 378, 199, 225 is 1.
Highest Common Factor of 378,199,225 is 1
Step 1: Since 378 > 199, we apply the division lemma to 378 and 199, to get
378 = 199 x 1 + 179
Step 2: Since the reminder 199 ≠ 0, we apply division lemma to 179 and 199, to get
199 = 179 x 1 + 20
Step 3: We consider the new divisor 179 and the new remainder 20, and apply the division lemma to get
179 = 20 x 8 + 19
We consider the new divisor 20 and the new remainder 19,and apply the division lemma to get
20 = 19 x 1 + 1
We consider the new divisor 19 and the new remainder 1,and apply the division lemma to get
19 = 1 x 19 + 0
The remainder has now become zero, so our procedure stops. Since the divisor at this stage is 1, the HCF of 378 and 199 is 1
Notice that 1 = HCF(19,1) = HCF(20,19) = HCF(179,20) = HCF(199,179) = HCF(378,199) .
We can take hcf of as 1st numbers and next number as another number to apply in Euclidean lemma
Step 1: Since 225 > 1, we apply the division lemma to 225 and 1, to get
225 = 1 x 225 + 0
The remainder has now become zero, so our procedure stops. Since the divisor at this stage is 1, the HCF of 1 and 225 is 1
Notice that 1 = HCF(225,1) .
HCF using Euclid's Algorithm Calculation Examples
Here are some samples of HCF using Euclid's Algorithm calculations.
Frequently Asked Questions on HCF of 378, 199, 225 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 378, 199, 225?
Answer: HCF of 378, 199, 225 is 1 the largest number that divides all the numbers leaving a remainder zero.
3. How to find HCF of 378, 199, 225 using Euclid's Algorithm?
Answer: For arbitrary numbers 378, 199, 225 apply Euclid’s Division Lemma in succession until you obtain a remainder zero. HCF is the remainder in the last but one step.