Highest Common Factor of 110, 7237 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 110, 7237 i.e. 1 the largest integer that leaves a remainder zero for all numbers.
HCF of 110, 7237 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 110, 7237 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 110, 7237 is 1.
HCF(110, 7237) = 1
HCF of 110, 7237 using Euclid's algorithm
Highest common factor or Highest common divisor (hcd) can be calculated by Euclid's algotithm.
Highest common factor (HCF) of 110, 7237 is 1.
Highest Common Factor of 110,7237 is 1
Step 1: Since 7237 > 110, we apply the division lemma to 7237 and 110, to get
7237 = 110 x 65 + 87
Step 2: Since the reminder 110 ≠ 0, we apply division lemma to 87 and 110, to get
110 = 87 x 1 + 23
Step 3: We consider the new divisor 87 and the new remainder 23, and apply the division lemma to get
87 = 23 x 3 + 18
We consider the new divisor 23 and the new remainder 18,and apply the division lemma to get
23 = 18 x 1 + 5
We consider the new divisor 18 and the new remainder 5,and apply the division lemma to get
18 = 5 x 3 + 3
We consider the new divisor 5 and the new remainder 3,and apply the division lemma to get
5 = 3 x 1 + 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 110 and 7237 is 1
Notice that 1 = HCF(2,1) = HCF(3,2) = HCF(5,3) = HCF(18,5) = HCF(23,18) = HCF(87,23) = HCF(110,87) = HCF(7237,110) .
HCF using Euclid's Algorithm Calculation Examples
Here are some samples of HCF using Euclid's Algorithm calculations.
Frequently Asked Questions on HCF of 110, 7237 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 110, 7237?
Answer: HCF of 110, 7237 is 1 the largest number that divides all the numbers leaving a remainder zero.
3. How to find HCF of 110, 7237 using Euclid's Algorithm?
Answer: For arbitrary numbers 110, 7237 apply Euclid’s Division Lemma in succession until you obtain a remainder zero. HCF is the remainder in the last but one step.