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, 9175, 2040 i.e. 1 the largest integer that leaves a remainder zero for all numbers.
HCF of 664, 9175, 2040 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, 9175, 2040 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, 9175, 2040 is 1.
HCF(664, 9175, 2040) = 1
Highest common factor or Highest common divisor (hcd) can be calculated by Euclid's algotithm.
Highest common factor (HCF) of 664, 9175, 2040 is 1.
Step 1: Since 9175 > 664, we apply the division lemma to 9175 and 664, to get
9175 = 664 x 13 + 543
Step 2: Since the reminder 664 ≠ 0, we apply division lemma to 543 and 664, to get
664 = 543 x 1 + 121
Step 3: We consider the new divisor 543 and the new remainder 121, and apply the division lemma to get
543 = 121 x 4 + 59
We consider the new divisor 121 and the new remainder 59,and apply the division lemma to get
121 = 59 x 2 + 3
We consider the new divisor 59 and the new remainder 3,and apply the division lemma to get
59 = 3 x 19 + 2
We consider the new divisor 3 and the new remainder 2,and apply the division lemma to get
3 = 2 x 1 + 1
We consider the new divisor 2 and the new remainder 1,and apply the division lemma to get
2 = 1 x 2 + 0
The remainder has now become zero, so our procedure stops. Since the divisor at this stage is 1, the HCF of 664 and 9175 is 1
Notice that 1 = HCF(2,1) = HCF(3,2) = HCF(59,3) = HCF(121,59) = HCF(543,121) = HCF(664,543) = HCF(9175,664) .
We can take hcf of as 1st numbers and next number as another number to apply in Euclidean lemma
Step 1: Since 2040 > 1, we apply the division lemma to 2040 and 1, to get
2040 = 1 x 2040 + 0
The remainder has now become zero, so our procedure stops. Since the divisor at this stage is 1, the HCF of 1 and 2040 is 1
Notice that 1 = HCF(2040,1) .
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, 9175, 2040?
Answer: HCF of 664, 9175, 2040 is 1 the largest number that divides all the numbers leaving a remainder zero.
3. How to find HCF of 664, 9175, 2040 using Euclid's Algorithm?
Answer: For arbitrary numbers 664, 9175, 2040 apply Euclid’s Division Lemma in succession until you obtain a remainder zero. HCF is the remainder in the last but one step.