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 504, 845, 242 i.e. 1 the largest integer that leaves a remainder zero for all numbers.
HCF of 504, 845, 242 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 504, 845, 242 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 504, 845, 242 is 1.
HCF(504, 845, 242) = 1
Highest common factor or Highest common divisor (hcd) can be calculated by Euclid's algotithm.
Highest common factor (HCF) of 504, 845, 242 is 1.
Step 1: Since 845 > 504, we apply the division lemma to 845 and 504, to get
845 = 504 x 1 + 341
Step 2: Since the reminder 504 ≠ 0, we apply division lemma to 341 and 504, to get
504 = 341 x 1 + 163
Step 3: We consider the new divisor 341 and the new remainder 163, and apply the division lemma to get
341 = 163 x 2 + 15
We consider the new divisor 163 and the new remainder 15,and apply the division lemma to get
163 = 15 x 10 + 13
We consider the new divisor 15 and the new remainder 13,and apply the division lemma to get
15 = 13 x 1 + 2
We consider the new divisor 13 and the new remainder 2,and apply the division lemma to get
13 = 2 x 6 + 1
We consider the new divisor 2 and the new remainder 1,and apply the division lemma to get
2 = 1 x 2 + 0
The remainder has now become zero, so our procedure stops. Since the divisor at this stage is 1, the HCF of 504 and 845 is 1
Notice that 1 = HCF(2,1) = HCF(13,2) = HCF(15,13) = HCF(163,15) = HCF(341,163) = HCF(504,341) = HCF(845,504) .
We can take hcf of as 1st numbers and next number as another number to apply in Euclidean lemma
Step 1: Since 242 > 1, we apply the division lemma to 242 and 1, to get
242 = 1 x 242 + 0
The remainder has now become zero, so our procedure stops. Since the divisor at this stage is 1, the HCF of 1 and 242 is 1
Notice that 1 = HCF(242,1) .
Here are some samples of HCF using Euclid's Algorithm calculations.
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 504, 845, 242?
Answer: HCF of 504, 845, 242 is 1 the largest number that divides all the numbers leaving a remainder zero.
3. How to find HCF of 504, 845, 242 using Euclid's Algorithm?
Answer: For arbitrary numbers 504, 845, 242 apply Euclid’s Division Lemma in succession until you obtain a remainder zero. HCF is the remainder in the last but one step.