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, 511, 657 i.e. 1 the largest integer that leaves a remainder zero for all numbers.
HCF of 194, 511, 657 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, 511, 657 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, 511, 657 is 1.
HCF(194, 511, 657) = 1
Highest common factor or Highest common divisor (hcd) can be calculated by Euclid's algotithm.
Highest common factor (HCF) of 194, 511, 657 is 1.
Step 1: Since 511 > 194, we apply the division lemma to 511 and 194, to get
511 = 194 x 2 + 123
Step 2: Since the reminder 194 ≠ 0, we apply division lemma to 123 and 194, to get
194 = 123 x 1 + 71
Step 3: We consider the new divisor 123 and the new remainder 71, and apply the division lemma to get
123 = 71 x 1 + 52
We consider the new divisor 71 and the new remainder 52,and apply the division lemma to get
71 = 52 x 1 + 19
We consider the new divisor 52 and the new remainder 19,and apply the division lemma to get
52 = 19 x 2 + 14
We consider the new divisor 19 and the new remainder 14,and apply the division lemma to get
19 = 14 x 1 + 5
We consider the new divisor 14 and the new remainder 5,and apply the division lemma to get
14 = 5 x 2 + 4
We consider the new divisor 5 and the new remainder 4,and apply the division lemma to get
5 = 4 x 1 + 1
We consider the new divisor 4 and the new remainder 1,and apply the division lemma to get
4 = 1 x 4 + 0
The remainder has now become zero, so our procedure stops. Since the divisor at this stage is 1, the HCF of 194 and 511 is 1
Notice that 1 = HCF(4,1) = HCF(5,4) = HCF(14,5) = HCF(19,14) = HCF(52,19) = HCF(71,52) = HCF(123,71) = HCF(194,123) = HCF(511,194) .
We can take hcf of as 1st numbers and next number as another number to apply in Euclidean lemma
Step 1: Since 657 > 1, we apply the division lemma to 657 and 1, to get
657 = 1 x 657 + 0
The remainder has now become zero, so our procedure stops. Since the divisor at this stage is 1, the HCF of 1 and 657 is 1
Notice that 1 = HCF(657,1) .
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 194, 511, 657?
Answer: HCF of 194, 511, 657 is 1 the largest number that divides all the numbers leaving a remainder zero.
3. How to find HCF of 194, 511, 657 using Euclid's Algorithm?
Answer: For arbitrary numbers 194, 511, 657 apply Euclid’s Division Lemma in succession until you obtain a remainder zero. HCF is the remainder in the last but one step.