Highest Common Factor of 116, 535 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 116, 535 i.e. 1 the largest integer that leaves a remainder zero for all numbers.
HCF of 116, 535 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 116, 535 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 116, 535 is 1.
HCF(116, 535) = 1
HCF of 116, 535 using Euclid's algorithm
Highest common factor or Highest common divisor (hcd) can be calculated by Euclid's algotithm.
Highest common factor (HCF) of 116, 535 is 1.
Highest Common Factor of 116,535 is 1
Step 1: Since 535 > 116, we apply the division lemma to 535 and 116, to get
535 = 116 x 4 + 71
Step 2: Since the reminder 116 ≠ 0, we apply division lemma to 71 and 116, to get
116 = 71 x 1 + 45
Step 3: We consider the new divisor 71 and the new remainder 45, and apply the division lemma to get
71 = 45 x 1 + 26
We consider the new divisor 45 and the new remainder 26,and apply the division lemma to get
45 = 26 x 1 + 19
We consider the new divisor 26 and the new remainder 19,and apply the division lemma to get
26 = 19 x 1 + 7
We consider the new divisor 19 and the new remainder 7,and apply the division lemma to get
19 = 7 x 2 + 5
We consider the new divisor 7 and the new remainder 5,and apply the division lemma to get
7 = 5 x 1 + 2
We consider the new divisor 5 and the new remainder 2,and apply the division lemma to get
5 = 2 x 2 + 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 116 and 535 is 1
Notice that 1 = HCF(2,1) = HCF(5,2) = HCF(7,5) = HCF(19,7) = HCF(26,19) = HCF(45,26) = HCF(71,45) = HCF(116,71) = HCF(535,116) .
HCF using Euclid's Algorithm Calculation Examples
Here are some samples of HCF using Euclid's Algorithm calculations.
Frequently Asked Questions on HCF of 116, 535 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 116, 535?
Answer: HCF of 116, 535 is 1 the largest number that divides all the numbers leaving a remainder zero.
3. How to find HCF of 116, 535 using Euclid's Algorithm?
Answer: For arbitrary numbers 116, 535 apply Euclid’s Division Lemma in succession until you obtain a remainder zero. HCF is the remainder in the last but one step.