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 198, 439, 16 i.e. 1 the largest integer that leaves a remainder zero for all numbers.
HCF of 198, 439, 16 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 198, 439, 16 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 198, 439, 16 is 1.
HCF(198, 439, 16) = 1
Highest common factor or Highest common divisor (hcd) can be calculated by Euclid's algotithm.
Highest common factor (HCF) of 198, 439, 16 is 1.
Step 1: Since 439 > 198, we apply the division lemma to 439 and 198, to get
439 = 198 x 2 + 43
Step 2: Since the reminder 198 ≠ 0, we apply division lemma to 43 and 198, to get
198 = 43 x 4 + 26
Step 3: We consider the new divisor 43 and the new remainder 26, and apply the division lemma to get
43 = 26 x 1 + 17
We consider the new divisor 26 and the new remainder 17,and apply the division lemma to get
26 = 17 x 1 + 9
We consider the new divisor 17 and the new remainder 9,and apply the division lemma to get
17 = 9 x 1 + 8
We consider the new divisor 9 and the new remainder 8,and apply the division lemma to get
9 = 8 x 1 + 1
We consider the new divisor 8 and the new remainder 1,and apply the division lemma to get
8 = 1 x 8 + 0
The remainder has now become zero, so our procedure stops. Since the divisor at this stage is 1, the HCF of 198 and 439 is 1
Notice that 1 = HCF(8,1) = HCF(9,8) = HCF(17,9) = HCF(26,17) = HCF(43,26) = HCF(198,43) = HCF(439,198) .
We can take hcf of as 1st numbers and next number as another number to apply in Euclidean lemma
Step 1: Since 16 > 1, we apply the division lemma to 16 and 1, to get
16 = 1 x 16 + 0
The remainder has now become zero, so our procedure stops. Since the divisor at this stage is 1, the HCF of 1 and 16 is 1
Notice that 1 = HCF(16,1) .
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 198, 439, 16?
Answer: HCF of 198, 439, 16 is 1 the largest number that divides all the numbers leaving a remainder zero.
3. How to find HCF of 198, 439, 16 using Euclid's Algorithm?
Answer: For arbitrary numbers 198, 439, 16 apply Euclid’s Division Lemma in succession until you obtain a remainder zero. HCF is the remainder in the last but one step.