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 155, 860, 58 i.e. 1 the largest integer that leaves a remainder zero for all numbers.
HCF of 155, 860, 58 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 155, 860, 58 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 155, 860, 58 is 1.
HCF(155, 860, 58) = 1
Highest common factor or Highest common divisor (hcd) can be calculated by Euclid's algotithm.
Highest common factor (HCF) of 155, 860, 58 is 1.
Step 1: Since 860 > 155, we apply the division lemma to 860 and 155, to get
860 = 155 x 5 + 85
Step 2: Since the reminder 155 ≠ 0, we apply division lemma to 85 and 155, to get
155 = 85 x 1 + 70
Step 3: We consider the new divisor 85 and the new remainder 70, and apply the division lemma to get
85 = 70 x 1 + 15
We consider the new divisor 70 and the new remainder 15,and apply the division lemma to get
70 = 15 x 4 + 10
We consider the new divisor 15 and the new remainder 10,and apply the division lemma to get
15 = 10 x 1 + 5
We consider the new divisor 10 and the new remainder 5,and apply the division lemma to get
10 = 5 x 2 + 0
The remainder has now become zero, so our procedure stops. Since the divisor at this stage is 5, the HCF of 155 and 860 is 5
Notice that 5 = HCF(10,5) = HCF(15,10) = HCF(70,15) = HCF(85,70) = HCF(155,85) = HCF(860,155) .
We can take hcf of as 1st numbers and next number as another number to apply in Euclidean lemma
Step 1: Since 58 > 5, we apply the division lemma to 58 and 5, to get
58 = 5 x 11 + 3
Step 2: Since the reminder 5 ≠ 0, we apply division lemma to 3 and 5, to get
5 = 3 x 1 + 2
Step 3: 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 5 and 58 is 1
Notice that 1 = HCF(2,1) = HCF(3,2) = HCF(5,3) = HCF(58,5) .
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 155, 860, 58?
Answer: HCF of 155, 860, 58 is 1 the largest number that divides all the numbers leaving a remainder zero.
3. How to find HCF of 155, 860, 58 using Euclid's Algorithm?
Answer: For arbitrary numbers 155, 860, 58 apply Euclid’s Division Lemma in succession until you obtain a remainder zero. HCF is the remainder in the last but one step.