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 558, 986, 58 i.e. 2 the largest integer that leaves a remainder zero for all numbers.
HCF of 558, 986, 58 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 558, 986, 58 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 558, 986, 58 is 2.
HCF(558, 986, 58) = 2
Highest common factor or Highest common divisor (hcd) can be calculated by Euclid's algotithm.
Highest common factor (HCF) of 558, 986, 58 is 2.
Step 1: Since 986 > 558, we apply the division lemma to 986 and 558, to get
986 = 558 x 1 + 428
Step 2: Since the reminder 558 ≠ 0, we apply division lemma to 428 and 558, to get
558 = 428 x 1 + 130
Step 3: We consider the new divisor 428 and the new remainder 130, and apply the division lemma to get
428 = 130 x 3 + 38
We consider the new divisor 130 and the new remainder 38,and apply the division lemma to get
130 = 38 x 3 + 16
We consider the new divisor 38 and the new remainder 16,and apply the division lemma to get
38 = 16 x 2 + 6
We consider the new divisor 16 and the new remainder 6,and apply the division lemma to get
16 = 6 x 2 + 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 558 and 986 is 2
Notice that 2 = HCF(4,2) = HCF(6,4) = HCF(16,6) = HCF(38,16) = HCF(130,38) = HCF(428,130) = HCF(558,428) = HCF(986,558) .
We can take hcf of as 1st numbers and next number as another number to apply in Euclidean lemma
Step 1: Since 58 > 2, we apply the division lemma to 58 and 2, to get
58 = 2 x 29 + 0
The remainder has now become zero, so our procedure stops. Since the divisor at this stage is 2, the HCF of 2 and 58 is 2
Notice that 2 = HCF(58,2) .
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 558, 986, 58?
Answer: HCF of 558, 986, 58 is 2 the largest number that divides all the numbers leaving a remainder zero.
3. How to find HCF of 558, 986, 58 using Euclid's Algorithm?
Answer: For arbitrary numbers 558, 986, 58 apply Euclid’s Division Lemma in succession until you obtain a remainder zero. HCF is the remainder in the last but one step.