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 617, 460 i.e. 1 the largest integer that leaves a remainder zero for all numbers.
HCF of 617, 460 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 617, 460 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 617, 460 is 1.
HCF(617, 460) = 1
Highest common factor or Highest common divisor (hcd) can be calculated by Euclid's algotithm.
Highest common factor (HCF) of 617, 460 is 1.
Step 1: Since 617 > 460, we apply the division lemma to 617 and 460, to get
617 = 460 x 1 + 157
Step 2: Since the reminder 460 ≠ 0, we apply division lemma to 157 and 460, to get
460 = 157 x 2 + 146
Step 3: We consider the new divisor 157 and the new remainder 146, and apply the division lemma to get
157 = 146 x 1 + 11
We consider the new divisor 146 and the new remainder 11,and apply the division lemma to get
146 = 11 x 13 + 3
We consider the new divisor 11 and the new remainder 3,and apply the division lemma to get
11 = 3 x 3 + 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 617 and 460 is 1
Notice that 1 = HCF(2,1) = HCF(3,2) = HCF(11,3) = HCF(146,11) = HCF(157,146) = HCF(460,157) = HCF(617,460) .
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 617, 460?
Answer: HCF of 617, 460 is 1 the largest number that divides all the numbers leaving a remainder zero.
3. How to find HCF of 617, 460 using Euclid's Algorithm?
Answer: For arbitrary numbers 617, 460 apply Euclid’s Division Lemma in succession until you obtain a remainder zero. HCF is the remainder in the last but one step.