Highest Common Factor of 359, 135 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 359, 135 i.e. 1 the largest integer that leaves a remainder zero for all numbers.
HCF of 359, 135 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 359, 135 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 359, 135 is 1.
HCF(359, 135) = 1
HCF of 359, 135 using Euclid's algorithm
Highest common factor or Highest common divisor (hcd) can be calculated by Euclid's algotithm.
Highest common factor (HCF) of 359, 135 is 1.
Highest Common Factor of 359,135 is 1
Step 1: Since 359 > 135, we apply the division lemma to 359 and 135, to get
359 = 135 x 2 + 89
Step 2: Since the reminder 135 ≠ 0, we apply division lemma to 89 and 135, to get
135 = 89 x 1 + 46
Step 3: We consider the new divisor 89 and the new remainder 46, and apply the division lemma to get
89 = 46 x 1 + 43
We consider the new divisor 46 and the new remainder 43,and apply the division lemma to get
46 = 43 x 1 + 3
We consider the new divisor 43 and the new remainder 3,and apply the division lemma to get
43 = 3 x 14 + 1
We consider the new divisor 3 and the new remainder 1,and apply the division lemma to get
3 = 1 x 3 + 0
The remainder has now become zero, so our procedure stops. Since the divisor at this stage is 1, the HCF of 359 and 135 is 1
Notice that 1 = HCF(3,1) = HCF(43,3) = HCF(46,43) = HCF(89,46) = HCF(135,89) = HCF(359,135) .
HCF using Euclid's Algorithm Calculation Examples
Here are some samples of HCF using Euclid's Algorithm calculations.
Frequently Asked Questions on HCF of 359, 135 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 359, 135?
Answer: HCF of 359, 135 is 1 the largest number that divides all the numbers leaving a remainder zero.
3. How to find HCF of 359, 135 using Euclid's Algorithm?
Answer: For arbitrary numbers 359, 135 apply Euclid’s Division Lemma in succession until you obtain a remainder zero. HCF is the remainder in the last but one step.