Highest Common Factor of 330, 735, 696 using Euclid's algorithm
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 330, 735, 696 i.e. 3 the largest integer that leaves a remainder zero for all numbers.
HCF of 330, 735, 696 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 330, 735, 696 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 330, 735, 696 is 3.
HCF(330, 735, 696) = 3
HCF of 330, 735, 696 using Euclid's algorithm
Highest common factor or Highest common divisor (hcd) can be calculated by Euclid's algotithm.
Highest common factor (HCF) of 330, 735, 696 is 3.
Highest Common Factor of 330,735,696 is 3
Step 1: Since 735 > 330, we apply the division lemma to 735 and 330, to get
735 = 330 x 2 + 75
Step 2: Since the reminder 330 ≠ 0, we apply division lemma to 75 and 330, to get
330 = 75 x 4 + 30
Step 3: We consider the new divisor 75 and the new remainder 30, and apply the division lemma to get
75 = 30 x 2 + 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 330 and 735 is 15
Notice that 15 = HCF(30,15) = HCF(75,30) = HCF(330,75) = HCF(735,330) .
We can take hcf of as 1st numbers and next number as another number to apply in Euclidean lemma
Step 1: Since 696 > 15, we apply the division lemma to 696 and 15, to get
696 = 15 x 46 + 6
Step 2: Since the reminder 15 ≠ 0, we apply division lemma to 6 and 15, to get
15 = 6 x 2 + 3
Step 3: We consider the new divisor 6 and the new remainder 3, and apply the division lemma to get
6 = 3 x 2 + 0
The remainder has now become zero, so our procedure stops. Since the divisor at this stage is 3, the HCF of 15 and 696 is 3
Notice that 3 = HCF(6,3) = HCF(15,6) = HCF(696,15) .
HCF using Euclid's Algorithm Calculation Examples
Here are some samples of HCF using Euclid's Algorithm calculations.
Frequently Asked Questions on HCF of 330, 735, 696 using Euclid's Algorithm
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 330, 735, 696?
Answer: HCF of 330, 735, 696 is 3 the largest number that divides all the numbers leaving a remainder zero.
3. How to find HCF of 330, 735, 696 using Euclid's Algorithm?
Answer: For arbitrary numbers 330, 735, 696 apply Euclid’s Division Lemma in succession until you obtain a remainder zero. HCF is the remainder in the last but one step.