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 7635, 6720 i.e. 15 the largest integer that leaves a remainder zero for all numbers.
HCF of 7635, 6720 is 15 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 7635, 6720 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 7635, 6720 is 15.
HCF(7635, 6720) = 15
Highest common factor or Highest common divisor (hcd) can be calculated by Euclid's algotithm.
Highest common factor (HCF) of 7635, 6720 is 15.
Step 1: Since 7635 > 6720, we apply the division lemma to 7635 and 6720, to get
7635 = 6720 x 1 + 915
Step 2: Since the reminder 6720 ≠ 0, we apply division lemma to 915 and 6720, to get
6720 = 915 x 7 + 315
Step 3: We consider the new divisor 915 and the new remainder 315, and apply the division lemma to get
915 = 315 x 2 + 285
We consider the new divisor 315 and the new remainder 285,and apply the division lemma to get
315 = 285 x 1 + 30
We consider the new divisor 285 and the new remainder 30,and apply the division lemma to get
285 = 30 x 9 + 15
We consider the new divisor 30 and the new remainder 15,and apply the division lemma to get
30 = 15 x 2 + 0
The remainder has now become zero, so our procedure stops. Since the divisor at this stage is 15, the HCF of 7635 and 6720 is 15
Notice that 15 = HCF(30,15) = HCF(285,30) = HCF(315,285) = HCF(915,315) = HCF(6720,915) = HCF(7635,6720) .
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 7635, 6720?
Answer: HCF of 7635, 6720 is 15 the largest number that divides all the numbers leaving a remainder zero.
3. How to find HCF of 7635, 6720 using Euclid's Algorithm?
Answer: For arbitrary numbers 7635, 6720 apply Euclid’s Division Lemma in succession until you obtain a remainder zero. HCF is the remainder in the last but one step.