Highest Common Factor of 173, 409, 678, 75 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 173, 409, 678, 75 i.e. 1 the largest integer that leaves a remainder zero for all numbers.
HCF of 173, 409, 678, 75 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 173, 409, 678, 75 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 173, 409, 678, 75 is 1.
HCF(173, 409, 678, 75) = 1
HCF of 173, 409, 678, 75 using Euclid's algorithm
Highest common factor or Highest common divisor (hcd) can be calculated by Euclid's algotithm.
Highest common factor (HCF) of 173, 409, 678, 75 is 1.
Highest Common Factor of 173,409,678,75 is 1
Step 1: Since 409 > 173, we apply the division lemma to 409 and 173, to get
409 = 173 x 2 + 63
Step 2: Since the reminder 173 ≠ 0, we apply division lemma to 63 and 173, to get
173 = 63 x 2 + 47
Step 3: We consider the new divisor 63 and the new remainder 47, and apply the division lemma to get
63 = 47 x 1 + 16
We consider the new divisor 47 and the new remainder 16,and apply the division lemma to get
47 = 16 x 2 + 15
We consider the new divisor 16 and the new remainder 15,and apply the division lemma to get
16 = 15 x 1 + 1
We consider the new divisor 15 and the new remainder 1,and apply the division lemma to get
15 = 1 x 15 + 0
The remainder has now become zero, so our procedure stops. Since the divisor at this stage is 1, the HCF of 173 and 409 is 1
Notice that 1 = HCF(15,1) = HCF(16,15) = HCF(47,16) = HCF(63,47) = HCF(173,63) = HCF(409,173) .
We can take hcf of as 1st numbers and next number as another number to apply in Euclidean lemma
Step 1: Since 678 > 1, we apply the division lemma to 678 and 1, to get
678 = 1 x 678 + 0
The remainder has now become zero, so our procedure stops. Since the divisor at this stage is 1, the HCF of 1 and 678 is 1
Notice that 1 = HCF(678,1) .
We can take hcf of as 1st numbers and next number as another number to apply in Euclidean lemma
Step 1: Since 75 > 1, we apply the division lemma to 75 and 1, to get
75 = 1 x 75 + 0
The remainder has now become zero, so our procedure stops. Since the divisor at this stage is 1, the HCF of 1 and 75 is 1
Notice that 1 = HCF(75,1) .
HCF using Euclid's Algorithm Calculation Examples
Here are some samples of HCF using Euclid's Algorithm calculations.
Frequently Asked Questions on HCF of 173, 409, 678, 75 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 173, 409, 678, 75?
Answer: HCF of 173, 409, 678, 75 is 1 the largest number that divides all the numbers leaving a remainder zero.
3. How to find HCF of 173, 409, 678, 75 using Euclid's Algorithm?
Answer: For arbitrary numbers 173, 409, 678, 75 apply Euclid’s Division Lemma in succession until you obtain a remainder zero. HCF is the remainder in the last but one step.