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 845, 546, 197 i.e. 1 the largest integer that leaves a remainder zero for all numbers.
HCF of 845, 546, 197 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 845, 546, 197 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 845, 546, 197 is 1.
HCF(845, 546, 197) = 1
Highest common factor or Highest common divisor (hcd) can be calculated by Euclid's algotithm.
Highest common factor (HCF) of 845, 546, 197 is 1.
Step 1: Since 845 > 546, we apply the division lemma to 845 and 546, to get
845 = 546 x 1 + 299
Step 2: Since the reminder 546 ≠ 0, we apply division lemma to 299 and 546, to get
546 = 299 x 1 + 247
Step 3: We consider the new divisor 299 and the new remainder 247, and apply the division lemma to get
299 = 247 x 1 + 52
We consider the new divisor 247 and the new remainder 52,and apply the division lemma to get
247 = 52 x 4 + 39
We consider the new divisor 52 and the new remainder 39,and apply the division lemma to get
52 = 39 x 1 + 13
We consider the new divisor 39 and the new remainder 13,and apply the division lemma to get
39 = 13 x 3 + 0
The remainder has now become zero, so our procedure stops. Since the divisor at this stage is 13, the HCF of 845 and 546 is 13
Notice that 13 = HCF(39,13) = HCF(52,39) = HCF(247,52) = HCF(299,247) = HCF(546,299) = HCF(845,546) .
We can take hcf of as 1st numbers and next number as another number to apply in Euclidean lemma
Step 1: Since 197 > 13, we apply the division lemma to 197 and 13, to get
197 = 13 x 15 + 2
Step 2: Since the reminder 13 ≠ 0, we apply division lemma to 2 and 13, to get
13 = 2 x 6 + 1
Step 3: 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 13 and 197 is 1
Notice that 1 = HCF(2,1) = HCF(13,2) = HCF(197,13) .
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 845, 546, 197?
Answer: HCF of 845, 546, 197 is 1 the largest number that divides all the numbers leaving a remainder zero.
3. How to find HCF of 845, 546, 197 using Euclid's Algorithm?
Answer: For arbitrary numbers 845, 546, 197 apply Euclid’s Division Lemma in succession until you obtain a remainder zero. HCF is the remainder in the last but one step.