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 574, 351, 172 i.e. 1 the largest integer that leaves a remainder zero for all numbers.
HCF of 574, 351, 172 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 574, 351, 172 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 574, 351, 172 is 1.
HCF(574, 351, 172) = 1
Highest common factor or Highest common divisor (hcd) can be calculated by Euclid's algotithm.
Highest common factor (HCF) of 574, 351, 172 is 1.
Step 1: Since 574 > 351, we apply the division lemma to 574 and 351, to get
574 = 351 x 1 + 223
Step 2: Since the reminder 351 ≠ 0, we apply division lemma to 223 and 351, to get
351 = 223 x 1 + 128
Step 3: We consider the new divisor 223 and the new remainder 128, and apply the division lemma to get
223 = 128 x 1 + 95
We consider the new divisor 128 and the new remainder 95,and apply the division lemma to get
128 = 95 x 1 + 33
We consider the new divisor 95 and the new remainder 33,and apply the division lemma to get
95 = 33 x 2 + 29
We consider the new divisor 33 and the new remainder 29,and apply the division lemma to get
33 = 29 x 1 + 4
We consider the new divisor 29 and the new remainder 4,and apply the division lemma to get
29 = 4 x 7 + 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 574 and 351 is 1
Notice that 1 = HCF(4,1) = HCF(29,4) = HCF(33,29) = HCF(95,33) = HCF(128,95) = HCF(223,128) = HCF(351,223) = HCF(574,351) .
We can take hcf of as 1st numbers and next number as another number to apply in Euclidean lemma
Step 1: Since 172 > 1, we apply the division lemma to 172 and 1, to get
172 = 1 x 172 + 0
The remainder has now become zero, so our procedure stops. Since the divisor at this stage is 1, the HCF of 1 and 172 is 1
Notice that 1 = HCF(172,1) .
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 574, 351, 172?
Answer: HCF of 574, 351, 172 is 1 the largest number that divides all the numbers leaving a remainder zero.
3. How to find HCF of 574, 351, 172 using Euclid's Algorithm?
Answer: For arbitrary numbers 574, 351, 172 apply Euclid’s Division Lemma in succession until you obtain a remainder zero. HCF is the remainder in the last but one step.