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 458, 285, 860 i.e. 1 the largest integer that leaves a remainder zero for all numbers.
HCF of 458, 285, 860 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 458, 285, 860 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 458, 285, 860 is 1.
HCF(458, 285, 860) = 1
Highest common factor or Highest common divisor (hcd) can be calculated by Euclid's algotithm.
Highest common factor (HCF) of 458, 285, 860 is 1.
Step 1: Since 458 > 285, we apply the division lemma to 458 and 285, to get
458 = 285 x 1 + 173
Step 2: Since the reminder 285 ≠ 0, we apply division lemma to 173 and 285, to get
285 = 173 x 1 + 112
Step 3: We consider the new divisor 173 and the new remainder 112, and apply the division lemma to get
173 = 112 x 1 + 61
We consider the new divisor 112 and the new remainder 61,and apply the division lemma to get
112 = 61 x 1 + 51
We consider the new divisor 61 and the new remainder 51,and apply the division lemma to get
61 = 51 x 1 + 10
We consider the new divisor 51 and the new remainder 10,and apply the division lemma to get
51 = 10 x 5 + 1
We consider the new divisor 10 and the new remainder 1,and apply the division lemma to get
10 = 1 x 10 + 0
The remainder has now become zero, so our procedure stops. Since the divisor at this stage is 1, the HCF of 458 and 285 is 1
Notice that 1 = HCF(10,1) = HCF(51,10) = HCF(61,51) = HCF(112,61) = HCF(173,112) = HCF(285,173) = HCF(458,285) .
We can take hcf of as 1st numbers and next number as another number to apply in Euclidean lemma
Step 1: Since 860 > 1, we apply the division lemma to 860 and 1, to get
860 = 1 x 860 + 0
The remainder has now become zero, so our procedure stops. Since the divisor at this stage is 1, the HCF of 1 and 860 is 1
Notice that 1 = HCF(860,1) .
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 458, 285, 860?
Answer: HCF of 458, 285, 860 is 1 the largest number that divides all the numbers leaving a remainder zero.
3. How to find HCF of 458, 285, 860 using Euclid's Algorithm?
Answer: For arbitrary numbers 458, 285, 860 apply Euclid’s Division Lemma in succession until you obtain a remainder zero. HCF is the remainder in the last but one step.