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, 6186, 3348 i.e. 6 the largest integer that leaves a remainder zero for all numbers.
HCF of 666, 6186, 3348 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 666, 6186, 3348 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, 6186, 3348 is 6.
HCF(666, 6186, 3348) = 6
Highest common factor or Highest common divisor (hcd) can be calculated by Euclid's algotithm.
Highest common factor (HCF) of 666, 6186, 3348 is 6.
Step 1: Since 6186 > 666, we apply the division lemma to 6186 and 666, to get
6186 = 666 x 9 + 192
Step 2: Since the reminder 666 ≠ 0, we apply division lemma to 192 and 666, to get
666 = 192 x 3 + 90
Step 3: We consider the new divisor 192 and the new remainder 90, and apply the division lemma to get
192 = 90 x 2 + 12
We consider the new divisor 90 and the new remainder 12,and apply the division lemma to get
90 = 12 x 7 + 6
We consider the new divisor 12 and the new remainder 6,and apply the division lemma to get
12 = 6 x 2 + 0
The remainder has now become zero, so our procedure stops. Since the divisor at this stage is 6, the HCF of 666 and 6186 is 6
Notice that 6 = HCF(12,6) = HCF(90,12) = HCF(192,90) = HCF(666,192) = HCF(6186,666) .
We can take hcf of as 1st numbers and next number as another number to apply in Euclidean lemma
Step 1: Since 3348 > 6, we apply the division lemma to 3348 and 6, to get
3348 = 6 x 558 + 0
The remainder has now become zero, so our procedure stops. Since the divisor at this stage is 6, the HCF of 6 and 3348 is 6
Notice that 6 = HCF(3348,6) .
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, 6186, 3348?
Answer: HCF of 666, 6186, 3348 is 6 the largest number that divides all the numbers leaving a remainder zero.
3. How to find HCF of 666, 6186, 3348 using Euclid's Algorithm?
Answer: For arbitrary numbers 666, 6186, 3348 apply Euclid’s Division Lemma in succession until you obtain a remainder zero. HCF is the remainder in the last but one step.