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 664, 981, 880 i.e. 1 the largest integer that leaves a remainder zero for all numbers.
HCF of 664, 981, 880 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 664, 981, 880 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 664, 981, 880 is 1.
HCF(664, 981, 880) = 1
Highest common factor or Highest common divisor (hcd) can be calculated by Euclid's algotithm.
Highest common factor (HCF) of 664, 981, 880 is 1.
Step 1: Since 981 > 664, we apply the division lemma to 981 and 664, to get
981 = 664 x 1 + 317
Step 2: Since the reminder 664 ≠ 0, we apply division lemma to 317 and 664, to get
664 = 317 x 2 + 30
Step 3: We consider the new divisor 317 and the new remainder 30, and apply the division lemma to get
317 = 30 x 10 + 17
We consider the new divisor 30 and the new remainder 17,and apply the division lemma to get
30 = 17 x 1 + 13
We consider the new divisor 17 and the new remainder 13,and apply the division lemma to get
17 = 13 x 1 + 4
We consider the new divisor 13 and the new remainder 4,and apply the division lemma to get
13 = 4 x 3 + 1
We consider the new divisor 4 and the new remainder 1,and apply the division lemma to get
4 = 1 x 4 + 0
The remainder has now become zero, so our procedure stops. Since the divisor at this stage is 1, the HCF of 664 and 981 is 1
Notice that 1 = HCF(4,1) = HCF(13,4) = HCF(17,13) = HCF(30,17) = HCF(317,30) = HCF(664,317) = HCF(981,664) .
We can take hcf of as 1st numbers and next number as another number to apply in Euclidean lemma
Step 1: Since 880 > 1, we apply the division lemma to 880 and 1, to get
880 = 1 x 880 + 0
The remainder has now become zero, so our procedure stops. Since the divisor at this stage is 1, the HCF of 1 and 880 is 1
Notice that 1 = HCF(880,1) .
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 664, 981, 880?
Answer: HCF of 664, 981, 880 is 1 the largest number that divides all the numbers leaving a remainder zero.
3. How to find HCF of 664, 981, 880 using Euclid's Algorithm?
Answer: For arbitrary numbers 664, 981, 880 apply Euclid’s Division Lemma in succession until you obtain a remainder zero. HCF is the remainder in the last but one step.