Highest Common Factor of 204, 1190, 1445 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 204, 1190, 1445 i.e. 17 the largest integer that leaves a remainder zero for all numbers.
HCF of 204, 1190, 1445 is 17 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 204, 1190, 1445 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 204, 1190, 1445 is 17.
HCF(204, 1190, 1445) = 17
HCF of 204, 1190, 1445 using Euclid's algorithm
Highest common factor or Highest common divisor (hcd) can be calculated by Euclid's algotithm.
Highest common factor (HCF) of 204, 1190, 1445 is 17.
Highest Common Factor of 204,1190,1445 is 17
Step 1: Since 1190 > 204, we apply the division lemma to 1190 and 204, to get
1190 = 204 x 5 + 170
Step 2: Since the reminder 204 ≠ 0, we apply division lemma to 170 and 204, to get
204 = 170 x 1 + 34
Step 3: We consider the new divisor 170 and the new remainder 34, and apply the division lemma to get
170 = 34 x 5 + 0
The remainder has now become zero, so our procedure stops. Since the divisor at this stage is 34, the HCF of 204 and 1190 is 34
Notice that 34 = HCF(170,34) = HCF(204,170) = HCF(1190,204) .
We can take hcf of as 1st numbers and next number as another number to apply in Euclidean lemma
Step 1: Since 1445 > 34, we apply the division lemma to 1445 and 34, to get
1445 = 34 x 42 + 17
Step 2: Since the reminder 34 ≠ 0, we apply division lemma to 17 and 34, to get
34 = 17 x 2 + 0
The remainder has now become zero, so our procedure stops. Since the divisor at this stage is 17, the HCF of 34 and 1445 is 17
Notice that 17 = HCF(34,17) = HCF(1445,34) .
HCF using Euclid's Algorithm Calculation Examples
Here are some samples of HCF using Euclid's Algorithm calculations.
Frequently Asked Questions on HCF of 204, 1190, 1445 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 204, 1190, 1445?
Answer: HCF of 204, 1190, 1445 is 17 the largest number that divides all the numbers leaving a remainder zero.
3. How to find HCF of 204, 1190, 1445 using Euclid's Algorithm?
Answer: For arbitrary numbers 204, 1190, 1445 apply Euclid’s Division Lemma in succession until you obtain a remainder zero. HCF is the remainder in the last but one step.