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 720, 852, 663 i.e. 3 the largest integer that leaves a remainder zero for all numbers.
HCF of 720, 852, 663 is 3 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 720, 852, 663 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 720, 852, 663 is 3.
HCF(720, 852, 663) = 3
Highest common factor or Highest common divisor (hcd) can be calculated by Euclid's algotithm.
Highest common factor (HCF) of 720, 852, 663 is 3.
Step 1: Since 852 > 720, we apply the division lemma to 852 and 720, to get
852 = 720 x 1 + 132
Step 2: Since the reminder 720 ≠ 0, we apply division lemma to 132 and 720, to get
720 = 132 x 5 + 60
Step 3: We consider the new divisor 132 and the new remainder 60, and apply the division lemma to get
132 = 60 x 2 + 12
We consider the new divisor 60 and the new remainder 12, and apply the division lemma to get
60 = 12 x 5 + 0
The remainder has now become zero, so our procedure stops. Since the divisor at this stage is 12, the HCF of 720 and 852 is 12
Notice that 12 = HCF(60,12) = HCF(132,60) = HCF(720,132) = HCF(852,720) .
We can take hcf of as 1st numbers and next number as another number to apply in Euclidean lemma
Step 1: Since 663 > 12, we apply the division lemma to 663 and 12, to get
663 = 12 x 55 + 3
Step 2: Since the reminder 12 ≠ 0, we apply division lemma to 3 and 12, to get
12 = 3 x 4 + 0
The remainder has now become zero, so our procedure stops. Since the divisor at this stage is 3, the HCF of 12 and 663 is 3
Notice that 3 = HCF(12,3) = HCF(663,12) .
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 720, 852, 663?
Answer: HCF of 720, 852, 663 is 3 the largest number that divides all the numbers leaving a remainder zero.
3. How to find HCF of 720, 852, 663 using Euclid's Algorithm?
Answer: For arbitrary numbers 720, 852, 663 apply Euclid’s Division Lemma in succession until you obtain a remainder zero. HCF is the remainder in the last but one step.