Highest Common Factor of 555, 905, 972, 394 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 555, 905, 972, 394 i.e. 1 the largest integer that leaves a remainder zero for all numbers.
HCF of 555, 905, 972, 394 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 555, 905, 972, 394 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 555, 905, 972, 394 is 1.
HCF(555, 905, 972, 394) = 1
HCF of 555, 905, 972, 394 using Euclid's algorithm
Highest common factor or Highest common divisor (hcd) can be calculated by Euclid's algotithm.
Highest common factor (HCF) of 555, 905, 972, 394 is 1.
Highest Common Factor of 555,905,972,394 is 1
Step 1: Since 905 > 555, we apply the division lemma to 905 and 555, to get
905 = 555 x 1 + 350
Step 2: Since the reminder 555 ≠ 0, we apply division lemma to 350 and 555, to get
555 = 350 x 1 + 205
Step 3: We consider the new divisor 350 and the new remainder 205, and apply the division lemma to get
350 = 205 x 1 + 145
We consider the new divisor 205 and the new remainder 145,and apply the division lemma to get
205 = 145 x 1 + 60
We consider the new divisor 145 and the new remainder 60,and apply the division lemma to get
145 = 60 x 2 + 25
We consider the new divisor 60 and the new remainder 25,and apply the division lemma to get
60 = 25 x 2 + 10
We consider the new divisor 25 and the new remainder 10,and apply the division lemma to get
25 = 10 x 2 + 5
We consider the new divisor 10 and the new remainder 5,and apply the division lemma to get
10 = 5 x 2 + 0
The remainder has now become zero, so our procedure stops. Since the divisor at this stage is 5, the HCF of 555 and 905 is 5
Notice that 5 = HCF(10,5) = HCF(25,10) = HCF(60,25) = HCF(145,60) = HCF(205,145) = HCF(350,205) = HCF(555,350) = HCF(905,555) .
We can take hcf of as 1st numbers and next number as another number to apply in Euclidean lemma
Step 1: Since 972 > 5, we apply the division lemma to 972 and 5, to get
972 = 5 x 194 + 2
Step 2: Since the reminder 5 ≠ 0, we apply division lemma to 2 and 5, to get
5 = 2 x 2 + 1
Step 3: 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 5 and 972 is 1
Notice that 1 = HCF(2,1) = HCF(5,2) = HCF(972,5) .
We can take hcf of as 1st numbers and next number as another number to apply in Euclidean lemma
Step 1: Since 394 > 1, we apply the division lemma to 394 and 1, to get
394 = 1 x 394 + 0
The remainder has now become zero, so our procedure stops. Since the divisor at this stage is 1, the HCF of 1 and 394 is 1
Notice that 1 = HCF(394,1) .
HCF using Euclid's Algorithm Calculation Examples
Here are some samples of HCF using Euclid's Algorithm calculations.
Frequently Asked Questions on HCF of 555, 905, 972, 394 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 555, 905, 972, 394?
Answer: HCF of 555, 905, 972, 394 is 1 the largest number that divides all the numbers leaving a remainder zero.
3. How to find HCF of 555, 905, 972, 394 using Euclid's Algorithm?
Answer: For arbitrary numbers 555, 905, 972, 394 apply Euclid’s Division Lemma in succession until you obtain a remainder zero. HCF is the remainder in the last but one step.
