Highest Common Factor of 661, 720, 321 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 661, 720, 321 i.e. 1 the largest integer that leaves a remainder zero for all numbers.
HCF of 661, 720, 321 is 1 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 661, 720, 321 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 661, 720, 321 is 1.
HCF(661, 720, 321) = 1
HCF of 661, 720, 321 using Euclid's algorithm
Highest common factor or Highest common divisor (hcd) can be calculated by Euclid's algotithm.
Highest common factor (HCF) of 661, 720, 321 is 1.
Highest Common Factor of 661,720,321 is 1
Step 1: Since 720 > 661, we apply the division lemma to 720 and 661, to get
720 = 661 x 1 + 59
Step 2: Since the reminder 661 ≠ 0, we apply division lemma to 59 and 661, to get
661 = 59 x 11 + 12
Step 3: We consider the new divisor 59 and the new remainder 12, and apply the division lemma to get
59 = 12 x 4 + 11
We consider the new divisor 12 and the new remainder 11,and apply the division lemma to get
12 = 11 x 1 + 1
We consider the new divisor 11 and the new remainder 1,and apply the division lemma to get
11 = 1 x 11 + 0
The remainder has now become zero, so our procedure stops. Since the divisor at this stage is 1, the HCF of 661 and 720 is 1
Notice that 1 = HCF(11,1) = HCF(12,11) = HCF(59,12) = HCF(661,59) = HCF(720,661) .
We can take hcf of as 1st numbers and next number as another number to apply in Euclidean lemma
Step 1: Since 321 > 1, we apply the division lemma to 321 and 1, to get
321 = 1 x 321 + 0
The remainder has now become zero, so our procedure stops. Since the divisor at this stage is 1, the HCF of 1 and 321 is 1
Notice that 1 = HCF(321,1) .
HCF using Euclid's Algorithm Calculation Examples
Here are some samples of HCF using Euclid's Algorithm calculations.
Frequently Asked Questions on HCF of 661, 720, 321 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 661, 720, 321?
Answer: HCF of 661, 720, 321 is 1 the largest number that divides all the numbers leaving a remainder zero.
3. How to find HCF of 661, 720, 321 using Euclid's Algorithm?
Answer: For arbitrary numbers 661, 720, 321 apply Euclid’s Division Lemma in succession until you obtain a remainder zero. HCF is the remainder in the last but one step.