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 194, 315 i.e. 1 the largest integer that leaves a remainder zero for all numbers.
HCF of 194, 315 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 194, 315 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 194, 315 is 1.
HCF(194, 315) = 1
Highest common factor or Highest common divisor (hcd) can be calculated by Euclid's algotithm.
Highest common factor (HCF) of 194, 315 is 1.
Step 1: Since 315 > 194, we apply the division lemma to 315 and 194, to get
315 = 194 x 1 + 121
Step 2: Since the reminder 194 ≠ 0, we apply division lemma to 121 and 194, to get
194 = 121 x 1 + 73
Step 3: We consider the new divisor 121 and the new remainder 73, and apply the division lemma to get
121 = 73 x 1 + 48
We consider the new divisor 73 and the new remainder 48,and apply the division lemma to get
73 = 48 x 1 + 25
We consider the new divisor 48 and the new remainder 25,and apply the division lemma to get
48 = 25 x 1 + 23
We consider the new divisor 25 and the new remainder 23,and apply the division lemma to get
25 = 23 x 1 + 2
We consider the new divisor 23 and the new remainder 2,and apply the division lemma to get
23 = 2 x 11 + 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 194 and 315 is 1
Notice that 1 = HCF(2,1) = HCF(23,2) = HCF(25,23) = HCF(48,25) = HCF(73,48) = HCF(121,73) = HCF(194,121) = HCF(315,194) .
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 194, 315?
Answer: HCF of 194, 315 is 1 the largest number that divides all the numbers leaving a remainder zero.
3. How to find HCF of 194, 315 using Euclid's Algorithm?
Answer: For arbitrary numbers 194, 315 apply Euclid’s Division Lemma in succession until you obtain a remainder zero. HCF is the remainder in the last but one step.