Highest Common Factor of 75, 40, 43, 31 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 75, 40, 43, 31 i.e. 1 the largest integer that leaves a remainder zero for all numbers.
HCF of 75, 40, 43, 31 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 75, 40, 43, 31 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 75, 40, 43, 31 is 1.
HCF(75, 40, 43, 31) = 1
HCF of 75, 40, 43, 31 using Euclid's algorithm
Highest common factor or Highest common divisor (hcd) can be calculated by Euclid's algotithm.
Highest common factor (HCF) of 75, 40, 43, 31 is 1.
Highest Common Factor of 75,40,43,31 is 1
Step 1: Since 75 > 40, we apply the division lemma to 75 and 40, to get
75 = 40 x 1 + 35
Step 2: Since the reminder 40 ≠ 0, we apply division lemma to 35 and 40, to get
40 = 35 x 1 + 5
Step 3: We consider the new divisor 35 and the new remainder 5, and apply the division lemma to get
35 = 5 x 7 + 0
The remainder has now become zero, so our procedure stops. Since the divisor at this stage is 5, the HCF of 75 and 40 is 5
Notice that 5 = HCF(35,5) = HCF(40,35) = HCF(75,40) .
We can take hcf of as 1st numbers and next number as another number to apply in Euclidean lemma
Step 1: Since 43 > 5, we apply the division lemma to 43 and 5, to get
43 = 5 x 8 + 3
Step 2: Since the reminder 5 ≠ 0, we apply division lemma to 3 and 5, to get
5 = 3 x 1 + 2
Step 3: 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 5 and 43 is 1
Notice that 1 = HCF(2,1) = HCF(3,2) = HCF(5,3) = HCF(43,5) .
We can take hcf of as 1st numbers and next number as another number to apply in Euclidean lemma
Step 1: Since 31 > 1, we apply the division lemma to 31 and 1, to get
31 = 1 x 31 + 0
The remainder has now become zero, so our procedure stops. Since the divisor at this stage is 1, the HCF of 1 and 31 is 1
Notice that 1 = HCF(31,1) .
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Frequently Asked Questions on HCF of 75, 40, 43, 31 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 75, 40, 43, 31?
Answer: HCF of 75, 40, 43, 31 is 1 the largest number that divides all the numbers leaving a remainder zero.
3. How to find HCF of 75, 40, 43, 31 using Euclid's Algorithm?
Answer: For arbitrary numbers 75, 40, 43, 31 apply Euclid’s Division Lemma in succession until you obtain a remainder zero. HCF is the remainder in the last but one step.