Highest Common Factor of 117, 610, 359 using Euclid's algorithm
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 117, 610, 359 i.e. 1 the largest integer that leaves a remainder zero for all numbers.
HCF of 117, 610, 359 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 117, 610, 359 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 117, 610, 359 is 1.
HCF(117, 610, 359) = 1
HCF of 117, 610, 359 using Euclid's algorithm
Highest common factor or Highest common divisor (hcd) can be calculated by Euclid's algotithm.
Highest common factor (HCF) of 117, 610, 359 is 1.
Highest Common Factor of 117,610,359 is 1
Step 1: Since 610 > 117, we apply the division lemma to 610 and 117, to get
610 = 117 x 5 + 25
Step 2: Since the reminder 117 ≠ 0, we apply division lemma to 25 and 117, to get
117 = 25 x 4 + 17
Step 3: We consider the new divisor 25 and the new remainder 17, and apply the division lemma to get
25 = 17 x 1 + 8
We consider the new divisor 17 and the new remainder 8,and apply the division lemma to get
17 = 8 x 2 + 1
We consider the new divisor 8 and the new remainder 1,and apply the division lemma to get
8 = 1 x 8 + 0
The remainder has now become zero, so our procedure stops. Since the divisor at this stage is 1, the HCF of 117 and 610 is 1
Notice that 1 = HCF(8,1) = HCF(17,8) = HCF(25,17) = HCF(117,25) = HCF(610,117) .
We can take hcf of as 1st numbers and next number as another number to apply in Euclidean lemma
Step 1: Since 359 > 1, we apply the division lemma to 359 and 1, to get
359 = 1 x 359 + 0
The remainder has now become zero, so our procedure stops. Since the divisor at this stage is 1, the HCF of 1 and 359 is 1
Notice that 1 = HCF(359,1) .
HCF using Euclid's Algorithm Calculation Examples
Here are some samples of HCF using Euclid's Algorithm calculations.
Frequently Asked Questions on HCF of 117, 610, 359 using Euclid's Algorithm
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 117, 610, 359?
Answer: HCF of 117, 610, 359 is 1 the largest number that divides all the numbers leaving a remainder zero.
3. How to find HCF of 117, 610, 359 using Euclid's Algorithm?
Answer: For arbitrary numbers 117, 610, 359 apply Euclid’s Division Lemma in succession until you obtain a remainder zero. HCF is the remainder in the last but one step.