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 222, 582, 108 i.e. 6 the largest integer that leaves a remainder zero for all numbers.
HCF of 222, 582, 108 is 6 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 222, 582, 108 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 222, 582, 108 is 6.
HCF(222, 582, 108) = 6
Highest common factor or Highest common divisor (hcd) can be calculated by Euclid's algotithm.
Highest common factor (HCF) of 222, 582, 108 is 6.
Step 1: Since 582 > 222, we apply the division lemma to 582 and 222, to get
582 = 222 x 2 + 138
Step 2: Since the reminder 222 ≠ 0, we apply division lemma to 138 and 222, to get
222 = 138 x 1 + 84
Step 3: We consider the new divisor 138 and the new remainder 84, and apply the division lemma to get
138 = 84 x 1 + 54
We consider the new divisor 84 and the new remainder 54,and apply the division lemma to get
84 = 54 x 1 + 30
We consider the new divisor 54 and the new remainder 30,and apply the division lemma to get
54 = 30 x 1 + 24
We consider the new divisor 30 and the new remainder 24,and apply the division lemma to get
30 = 24 x 1 + 6
We consider the new divisor 24 and the new remainder 6,and apply the division lemma to get
24 = 6 x 4 + 0
The remainder has now become zero, so our procedure stops. Since the divisor at this stage is 6, the HCF of 222 and 582 is 6
Notice that 6 = HCF(24,6) = HCF(30,24) = HCF(54,30) = HCF(84,54) = HCF(138,84) = HCF(222,138) = HCF(582,222) .
We can take hcf of as 1st numbers and next number as another number to apply in Euclidean lemma
Step 1: Since 108 > 6, we apply the division lemma to 108 and 6, to get
108 = 6 x 18 + 0
The remainder has now become zero, so our procedure stops. Since the divisor at this stage is 6, the HCF of 6 and 108 is 6
Notice that 6 = HCF(108,6) .
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 222, 582, 108?
Answer: HCF of 222, 582, 108 is 6 the largest number that divides all the numbers leaving a remainder zero.
3. How to find HCF of 222, 582, 108 using Euclid's Algorithm?
Answer: For arbitrary numbers 222, 582, 108 apply Euclid’s Division Lemma in succession until you obtain a remainder zero. HCF is the remainder in the last but one step.