Highest Common Factor of 168, 549, 417 using Euclid's algorithm
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 168, 549, 417 i.e. 3 the largest integer that leaves a remainder zero for all numbers.
HCF of 168, 549, 417 is 3 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 168, 549, 417 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 168, 549, 417 is 3.
HCF(168, 549, 417) = 3
HCF of 168, 549, 417 using Euclid's algorithm
Highest common factor or Highest common divisor (hcd) can be calculated by Euclid's algotithm.
Highest common factor (HCF) of 168, 549, 417 is 3.
Highest Common Factor of 168,549,417 is 3
Step 1: Since 549 > 168, we apply the division lemma to 549 and 168, to get
549 = 168 x 3 + 45
Step 2: Since the reminder 168 ≠ 0, we apply division lemma to 45 and 168, to get
168 = 45 x 3 + 33
Step 3: We consider the new divisor 45 and the new remainder 33, and apply the division lemma to get
45 = 33 x 1 + 12
We consider the new divisor 33 and the new remainder 12,and apply the division lemma to get
33 = 12 x 2 + 9
We consider the new divisor 12 and the new remainder 9,and apply the division lemma to get
12 = 9 x 1 + 3
We consider the new divisor 9 and the new remainder 3,and apply the division lemma to get
9 = 3 x 3 + 0
The remainder has now become zero, so our procedure stops. Since the divisor at this stage is 3, the HCF of 168 and 549 is 3
Notice that 3 = HCF(9,3) = HCF(12,9) = HCF(33,12) = HCF(45,33) = HCF(168,45) = HCF(549,168) .
We can take hcf of as 1st numbers and next number as another number to apply in Euclidean lemma
Step 1: Since 417 > 3, we apply the division lemma to 417 and 3, to get
417 = 3 x 139 + 0
The remainder has now become zero, so our procedure stops. Since the divisor at this stage is 3, the HCF of 3 and 417 is 3
Notice that 3 = HCF(417,3) .
HCF using Euclid's Algorithm Calculation Examples
Here are some samples of HCF using Euclid's Algorithm calculations.
Frequently Asked Questions on HCF of 168, 549, 417 using Euclid's Algorithm
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 168, 549, 417?
Answer: HCF of 168, 549, 417 is 3 the largest number that divides all the numbers leaving a remainder zero.
3. How to find HCF of 168, 549, 417 using Euclid's Algorithm?
Answer: For arbitrary numbers 168, 549, 417 apply Euclid’s Division Lemma in succession until you obtain a remainder zero. HCF is the remainder in the last but one step.