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 171, 640, 687 i.e. 1 the largest integer that leaves a remainder zero for all numbers.
HCF of 171, 640, 687 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 171, 640, 687 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 171, 640, 687 is 1.
HCF(171, 640, 687) = 1
Highest common factor or Highest common divisor (hcd) can be calculated by Euclid's algotithm.
Highest common factor (HCF) of 171, 640, 687 is 1.
Step 1: Since 640 > 171, we apply the division lemma to 640 and 171, to get
640 = 171 x 3 + 127
Step 2: Since the reminder 171 ≠ 0, we apply division lemma to 127 and 171, to get
171 = 127 x 1 + 44
Step 3: We consider the new divisor 127 and the new remainder 44, and apply the division lemma to get
127 = 44 x 2 + 39
We consider the new divisor 44 and the new remainder 39,and apply the division lemma to get
44 = 39 x 1 + 5
We consider the new divisor 39 and the new remainder 5,and apply the division lemma to get
39 = 5 x 7 + 4
We consider the new divisor 5 and the new remainder 4,and apply the division lemma to get
5 = 4 x 1 + 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 171 and 640 is 1
Notice that 1 = HCF(4,1) = HCF(5,4) = HCF(39,5) = HCF(44,39) = HCF(127,44) = HCF(171,127) = HCF(640,171) .
We can take hcf of as 1st numbers and next number as another number to apply in Euclidean lemma
Step 1: Since 687 > 1, we apply the division lemma to 687 and 1, to get
687 = 1 x 687 + 0
The remainder has now become zero, so our procedure stops. Since the divisor at this stage is 1, the HCF of 1 and 687 is 1
Notice that 1 = HCF(687,1) .
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 171, 640, 687?
Answer: HCF of 171, 640, 687 is 1 the largest number that divides all the numbers leaving a remainder zero.
3. How to find HCF of 171, 640, 687 using Euclid's Algorithm?
Answer: For arbitrary numbers 171, 640, 687 apply Euclid’s Division Lemma in succession until you obtain a remainder zero. HCF is the remainder in the last but one step.