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, 388, 63 i.e. 1 the largest integer that leaves a remainder zero for all numbers.
HCF of 666, 388, 63 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 666, 388, 63 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, 388, 63 is 1.
HCF(666, 388, 63) = 1
Highest common factor or Highest common divisor (hcd) can be calculated by Euclid's algotithm.
Highest common factor (HCF) of 666, 388, 63 is 1.
Step 1: Since 666 > 388, we apply the division lemma to 666 and 388, to get
666 = 388 x 1 + 278
Step 2: Since the reminder 388 ≠ 0, we apply division lemma to 278 and 388, to get
388 = 278 x 1 + 110
Step 3: We consider the new divisor 278 and the new remainder 110, and apply the division lemma to get
278 = 110 x 2 + 58
We consider the new divisor 110 and the new remainder 58,and apply the division lemma to get
110 = 58 x 1 + 52
We consider the new divisor 58 and the new remainder 52,and apply the division lemma to get
58 = 52 x 1 + 6
We consider the new divisor 52 and the new remainder 6,and apply the division lemma to get
52 = 6 x 8 + 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 666 and 388 is 2
Notice that 2 = HCF(4,2) = HCF(6,4) = HCF(52,6) = HCF(58,52) = HCF(110,58) = HCF(278,110) = HCF(388,278) = HCF(666,388) .
We can take hcf of as 1st numbers and next number as another number to apply in Euclidean lemma
Step 1: Since 63 > 2, we apply the division lemma to 63 and 2, to get
63 = 2 x 31 + 1
Step 2: Since the reminder 2 ≠ 0, we apply division lemma to 1 and 2, 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 2 and 63 is 1
Notice that 1 = HCF(2,1) = HCF(63,2) .
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 666, 388, 63?
Answer: HCF of 666, 388, 63 is 1 the largest number that divides all the numbers leaving a remainder zero.
3. How to find HCF of 666, 388, 63 using Euclid's Algorithm?
Answer: For arbitrary numbers 666, 388, 63 apply Euclid’s Division Lemma in succession until you obtain a remainder zero. HCF is the remainder in the last but one step.