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 175, 5057, 8450 i.e. 1 the largest integer that leaves a remainder zero for all numbers.
HCF of 175, 5057, 8450 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 175, 5057, 8450 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 175, 5057, 8450 is 1.
HCF(175, 5057, 8450) = 1
Highest common factor or Highest common divisor (hcd) can be calculated by Euclid's algotithm.
Highest common factor (HCF) of 175, 5057, 8450 is 1.
Step 1: Since 5057 > 175, we apply the division lemma to 5057 and 175, to get
5057 = 175 x 28 + 157
Step 2: Since the reminder 175 ≠ 0, we apply division lemma to 157 and 175, to get
175 = 157 x 1 + 18
Step 3: We consider the new divisor 157 and the new remainder 18, and apply the division lemma to get
157 = 18 x 8 + 13
We consider the new divisor 18 and the new remainder 13,and apply the division lemma to get
18 = 13 x 1 + 5
We consider the new divisor 13 and the new remainder 5,and apply the division lemma to get
13 = 5 x 2 + 3
We consider the new divisor 5 and the new remainder 3,and apply the division lemma to get
5 = 3 x 1 + 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 175 and 5057 is 1
Notice that 1 = HCF(2,1) = HCF(3,2) = HCF(5,3) = HCF(13,5) = HCF(18,13) = HCF(157,18) = HCF(175,157) = HCF(5057,175) .
We can take hcf of as 1st numbers and next number as another number to apply in Euclidean lemma
Step 1: Since 8450 > 1, we apply the division lemma to 8450 and 1, to get
8450 = 1 x 8450 + 0
The remainder has now become zero, so our procedure stops. Since the divisor at this stage is 1, the HCF of 1 and 8450 is 1
Notice that 1 = HCF(8450,1) .
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 175, 5057, 8450?
Answer: HCF of 175, 5057, 8450 is 1 the largest number that divides all the numbers leaving a remainder zero.
3. How to find HCF of 175, 5057, 8450 using Euclid's Algorithm?
Answer: For arbitrary numbers 175, 5057, 8450 apply Euclid’s Division Lemma in succession until you obtain a remainder zero. HCF is the remainder in the last but one step.