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 6705, 630 i.e. 45 the largest integer that leaves a remainder zero for all numbers.
HCF of 6705, 630 is 45 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 6705, 630 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 6705, 630 is 45.
HCF(6705, 630) = 45
Highest common factor or Highest common divisor (hcd) can be calculated by Euclid's algotithm.
Highest common factor (HCF) of 6705, 630 is 45.
Step 1: Since 6705 > 630, we apply the division lemma to 6705 and 630, to get
6705 = 630 x 10 + 405
Step 2: Since the reminder 630 ≠ 0, we apply division lemma to 405 and 630, to get
630 = 405 x 1 + 225
Step 3: We consider the new divisor 405 and the new remainder 225, and apply the division lemma to get
405 = 225 x 1 + 180
We consider the new divisor 225 and the new remainder 180,and apply the division lemma to get
225 = 180 x 1 + 45
We consider the new divisor 180 and the new remainder 45,and apply the division lemma to get
180 = 45 x 4 + 0
The remainder has now become zero, so our procedure stops. Since the divisor at this stage is 45, the HCF of 6705 and 630 is 45
Notice that 45 = HCF(180,45) = HCF(225,180) = HCF(405,225) = HCF(630,405) = HCF(6705,630) .
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 6705, 630?
Answer: HCF of 6705, 630 is 45 the largest number that divides all the numbers leaving a remainder zero.
3. How to find HCF of 6705, 630 using Euclid's Algorithm?
Answer: For arbitrary numbers 6705, 630 apply Euclid’s Division Lemma in succession until you obtain a remainder zero. HCF is the remainder in the last but one step.