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 666, 582, 352 i.e. 2 the largest integer that leaves a remainder zero for all numbers.
HCF of 666, 582, 352 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 666, 582, 352 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 666, 582, 352 is 2.
HCF(666, 582, 352) = 2
Highest common factor or Highest common divisor (hcd) can be calculated by Euclid's algotithm.
Highest common factor (HCF) of 666, 582, 352 is 2.
Step 1: Since 666 > 582, we apply the division lemma to 666 and 582, to get
666 = 582 x 1 + 84
Step 2: Since the reminder 582 ≠ 0, we apply division lemma to 84 and 582, to get
582 = 84 x 6 + 78
Step 3: We consider the new divisor 84 and the new remainder 78, and apply the division lemma to get
84 = 78 x 1 + 6
We consider the new divisor 78 and the new remainder 6, and apply the division lemma to get
78 = 6 x 13 + 0
The remainder has now become zero, so our procedure stops. Since the divisor at this stage is 6, the HCF of 666 and 582 is 6
Notice that 6 = HCF(78,6) = HCF(84,78) = HCF(582,84) = HCF(666,582) .
We can take hcf of as 1st numbers and next number as another number to apply in Euclidean lemma
Step 1: Since 352 > 6, we apply the division lemma to 352 and 6, to get
352 = 6 x 58 + 4
Step 2: Since the reminder 6 ≠ 0, we apply division lemma to 4 and 6, to get
6 = 4 x 1 + 2
Step 3: 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 6 and 352 is 2
Notice that 2 = HCF(4,2) = HCF(6,4) = HCF(352,6) .
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 666, 582, 352?
Answer: HCF of 666, 582, 352 is 2 the largest number that divides all the numbers leaving a remainder zero.
3. How to find HCF of 666, 582, 352 using Euclid's Algorithm?
Answer: For arbitrary numbers 666, 582, 352 apply Euclid’s Division Lemma in succession until you obtain a remainder zero. HCF is the remainder in the last but one step.