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 172, 988, 585 i.e. 1 the largest integer that leaves a remainder zero for all numbers.
HCF of 172, 988, 585 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 172, 988, 585 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 172, 988, 585 is 1.
HCF(172, 988, 585) = 1
Highest common factor or Highest common divisor (hcd) can be calculated by Euclid's algotithm.
Highest common factor (HCF) of 172, 988, 585 is 1.
Step 1: Since 988 > 172, we apply the division lemma to 988 and 172, to get
988 = 172 x 5 + 128
Step 2: Since the reminder 172 ≠ 0, we apply division lemma to 128 and 172, to get
172 = 128 x 1 + 44
Step 3: We consider the new divisor 128 and the new remainder 44, and apply the division lemma to get
128 = 44 x 2 + 40
We consider the new divisor 44 and the new remainder 40,and apply the division lemma to get
44 = 40 x 1 + 4
We consider the new divisor 40 and the new remainder 4,and apply the division lemma to get
40 = 4 x 10 + 0
The remainder has now become zero, so our procedure stops. Since the divisor at this stage is 4, the HCF of 172 and 988 is 4
Notice that 4 = HCF(40,4) = HCF(44,40) = HCF(128,44) = HCF(172,128) = HCF(988,172) .
We can take hcf of as 1st numbers and next number as another number to apply in Euclidean lemma
Step 1: Since 585 > 4, we apply the division lemma to 585 and 4, to get
585 = 4 x 146 + 1
Step 2: Since the reminder 4 ≠ 0, we apply division lemma to 1 and 4, 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 4 and 585 is 1
Notice that 1 = HCF(4,1) = HCF(585,4) .
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 172, 988, 585?
Answer: HCF of 172, 988, 585 is 1 the largest number that divides all the numbers leaving a remainder zero.
3. How to find HCF of 172, 988, 585 using Euclid's Algorithm?
Answer: For arbitrary numbers 172, 988, 585 apply Euclid’s Division Lemma in succession until you obtain a remainder zero. HCF is the remainder in the last but one step.