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 337, 545, 171 i.e. 1 the largest integer that leaves a remainder zero for all numbers.
HCF of 337, 545, 171 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 337, 545, 171 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 337, 545, 171 is 1.
HCF(337, 545, 171) = 1
Highest common factor or Highest common divisor (hcd) can be calculated by Euclid's algotithm.
Highest common factor (HCF) of 337, 545, 171 is 1.
Step 1: Since 545 > 337, we apply the division lemma to 545 and 337, to get
545 = 337 x 1 + 208
Step 2: Since the reminder 337 ≠ 0, we apply division lemma to 208 and 337, to get
337 = 208 x 1 + 129
Step 3: We consider the new divisor 208 and the new remainder 129, and apply the division lemma to get
208 = 129 x 1 + 79
We consider the new divisor 129 and the new remainder 79,and apply the division lemma to get
129 = 79 x 1 + 50
We consider the new divisor 79 and the new remainder 50,and apply the division lemma to get
79 = 50 x 1 + 29
We consider the new divisor 50 and the new remainder 29,and apply the division lemma to get
50 = 29 x 1 + 21
We consider the new divisor 29 and the new remainder 21,and apply the division lemma to get
29 = 21 x 1 + 8
We consider the new divisor 21 and the new remainder 8,and apply the division lemma to get
21 = 8 x 2 + 5
We consider the new divisor 8 and the new remainder 5,and apply the division lemma to get
8 = 5 x 1 + 3
We consider the new divisor 5 and the new remainder 3,and apply the division lemma to get
5 = 3 x 1 + 2
We consider the new divisor 3 and the new remainder 2,and apply the division lemma to get
3 = 2 x 1 + 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 337 and 545 is 1
Notice that 1 = HCF(2,1) = HCF(3,2) = HCF(5,3) = HCF(8,5) = HCF(21,8) = HCF(29,21) = HCF(50,29) = HCF(79,50) = HCF(129,79) = HCF(208,129) = HCF(337,208) = HCF(545,337) .
We can take hcf of as 1st numbers and next number as another number to apply in Euclidean lemma
Step 1: Since 171 > 1, we apply the division lemma to 171 and 1, to get
171 = 1 x 171 + 0
The remainder has now become zero, so our procedure stops. Since the divisor at this stage is 1, the HCF of 1 and 171 is 1
Notice that 1 = HCF(171,1) .
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 337, 545, 171?
Answer: HCF of 337, 545, 171 is 1 the largest number that divides all the numbers leaving a remainder zero.
3. How to find HCF of 337, 545, 171 using Euclid's Algorithm?
Answer: For arbitrary numbers 337, 545, 171 apply Euclid’s Division Lemma in succession until you obtain a remainder zero. HCF is the remainder in the last but one step.