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, 15345 i.e. 9 the largest integer that leaves a remainder zero for all numbers.
HCF of 666, 15345 is 9 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, 15345 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, 15345 is 9.
HCF(666, 15345) = 9
Highest common factor or Highest common divisor (hcd) can be calculated by Euclid's algotithm.
Highest common factor (HCF) of 666, 15345 is 9.
Step 1: Since 15345 > 666, we apply the division lemma to 15345 and 666, to get
15345 = 666 x 23 + 27
Step 2: Since the reminder 666 ≠ 0, we apply division lemma to 27 and 666, to get
666 = 27 x 24 + 18
Step 3: We consider the new divisor 27 and the new remainder 18, and apply the division lemma to get
27 = 18 x 1 + 9
We consider the new divisor 18 and the new remainder 9, and apply the division lemma to get
18 = 9 x 2 + 0
The remainder has now become zero, so our procedure stops. Since the divisor at this stage is 9, the HCF of 666 and 15345 is 9
Notice that 9 = HCF(18,9) = HCF(27,18) = HCF(666,27) = HCF(15345,666) .
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, 15345?
Answer: HCF of 666, 15345 is 9 the largest number that divides all the numbers leaving a remainder zero.
3. How to find HCF of 666, 15345 using Euclid's Algorithm?
Answer: For arbitrary numbers 666, 15345 apply Euclid’s Division Lemma in succession until you obtain a remainder zero. HCF is the remainder in the last but one step.