Highest Common Factor of 660, 398, 558 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 660, 398, 558 i.e. 2 the largest integer that leaves a remainder zero for all numbers.
HCF of 660, 398, 558 is 2 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 660, 398, 558 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 660, 398, 558 is 2.
HCF(660, 398, 558) = 2
HCF of 660, 398, 558 using Euclid's algorithm
Highest common factor or Highest common divisor (hcd) can be calculated by Euclid's algotithm.
Highest common factor (HCF) of 660, 398, 558 is 2.
Highest Common Factor of 660,398,558 is 2
Step 1: Since 660 > 398, we apply the division lemma to 660 and 398, to get
660 = 398 x 1 + 262
Step 2: Since the reminder 398 ≠ 0, we apply division lemma to 262 and 398, to get
398 = 262 x 1 + 136
Step 3: We consider the new divisor 262 and the new remainder 136, and apply the division lemma to get
262 = 136 x 1 + 126
We consider the new divisor 136 and the new remainder 126,and apply the division lemma to get
136 = 126 x 1 + 10
We consider the new divisor 126 and the new remainder 10,and apply the division lemma to get
126 = 10 x 12 + 6
We consider the new divisor 10 and the new remainder 6,and apply the division lemma to get
10 = 6 x 1 + 4
We consider the new divisor 6 and the new remainder 4,and apply the division lemma to get
6 = 4 x 1 + 2
We consider the new divisor 4 and the new remainder 2,and apply the division lemma to get
4 = 2 x 2 + 0
The remainder has now become zero, so our procedure stops. Since the divisor at this stage is 2, the HCF of 660 and 398 is 2
Notice that 2 = HCF(4,2) = HCF(6,4) = HCF(10,6) = HCF(126,10) = HCF(136,126) = HCF(262,136) = HCF(398,262) = HCF(660,398) .
We can take hcf of as 1st numbers and next number as another number to apply in Euclidean lemma
Step 1: Since 558 > 2, we apply the division lemma to 558 and 2, to get
558 = 2 x 279 + 0
The remainder has now become zero, so our procedure stops. Since the divisor at this stage is 2, the HCF of 2 and 558 is 2
Notice that 2 = HCF(558,2) .
HCF using Euclid's Algorithm Calculation Examples
Here are some samples of HCF using Euclid's Algorithm calculations.
Frequently Asked Questions on HCF of 660, 398, 558 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 660, 398, 558?
Answer: HCF of 660, 398, 558 is 2 the largest number that divides all the numbers leaving a remainder zero.
3. How to find HCF of 660, 398, 558 using Euclid's Algorithm?
Answer: For arbitrary numbers 660, 398, 558 apply Euclid’s Division Lemma in succession until you obtain a remainder zero. HCF is the remainder in the last but one step.