Highest Common Factor of 110, 40 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, 40 i.e. 10 the largest integer that leaves a remainder zero for all numbers.
HCF of 110, 40 is 10 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, 40 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, 40 is 10.
HCF(110, 40) = 10
HCF of 110, 40 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, 40 is 10.
Highest Common Factor of 110,40 is 10
Step 1: Since 110 > 40, we apply the division lemma to 110 and 40, to get
110 = 40 x 2 + 30
Step 2: Since the reminder 40 ≠ 0, we apply division lemma to 30 and 40, to get
40 = 30 x 1 + 10
Step 3: We consider the new divisor 30 and the new remainder 10, and apply the division lemma to get
30 = 10 x 3 + 0
The remainder has now become zero, so our procedure stops. Since the divisor at this stage is 10, the HCF of 110 and 40 is 10
Notice that 10 = HCF(30,10) = HCF(40,30) = HCF(110,40) .
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Frequently Asked Questions on HCF of 110, 40 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, 40?
Answer: HCF of 110, 40 is 10 the largest number that divides all the numbers leaving a remainder zero.
3. How to find HCF of 110, 40 using Euclid's Algorithm?
Answer: For arbitrary numbers 110, 40 apply Euclid’s Division Lemma in succession until you obtain a remainder zero. HCF is the remainder in the last but one step.