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 655, 258, 140 i.e. 1 the largest integer that leaves a remainder zero for all numbers.
HCF of 655, 258, 140 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 655, 258, 140 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 655, 258, 140 is 1.
HCF(655, 258, 140) = 1
Highest common factor or Highest common divisor (hcd) can be calculated by Euclid's algotithm.
Highest common factor (HCF) of 655, 258, 140 is 1.
Step 1: Since 655 > 258, we apply the division lemma to 655 and 258, to get
655 = 258 x 2 + 139
Step 2: Since the reminder 258 ≠ 0, we apply division lemma to 139 and 258, to get
258 = 139 x 1 + 119
Step 3: We consider the new divisor 139 and the new remainder 119, and apply the division lemma to get
139 = 119 x 1 + 20
We consider the new divisor 119 and the new remainder 20,and apply the division lemma to get
119 = 20 x 5 + 19
We consider the new divisor 20 and the new remainder 19,and apply the division lemma to get
20 = 19 x 1 + 1
We consider the new divisor 19 and the new remainder 1,and apply the division lemma to get
19 = 1 x 19 + 0
The remainder has now become zero, so our procedure stops. Since the divisor at this stage is 1, the HCF of 655 and 258 is 1
Notice that 1 = HCF(19,1) = HCF(20,19) = HCF(119,20) = HCF(139,119) = HCF(258,139) = HCF(655,258) .
We can take hcf of as 1st numbers and next number as another number to apply in Euclidean lemma
Step 1: Since 140 > 1, we apply the division lemma to 140 and 1, to get
140 = 1 x 140 + 0
The remainder has now become zero, so our procedure stops. Since the divisor at this stage is 1, the HCF of 1 and 140 is 1
Notice that 1 = HCF(140,1) .
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 655, 258, 140?
Answer: HCF of 655, 258, 140 is 1 the largest number that divides all the numbers leaving a remainder zero.
3. How to find HCF of 655, 258, 140 using Euclid's Algorithm?
Answer: For arbitrary numbers 655, 258, 140 apply Euclid’s Division Lemma in succession until you obtain a remainder zero. HCF is the remainder in the last but one step.