Highest Common Factor of 31, 74, 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 31, 74, 40 i.e. 1 the largest integer that leaves a remainder zero for all numbers.
HCF of 31, 74, 40 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 31, 74, 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 31, 74, 40 is 1.
HCF(31, 74, 40) = 1
HCF of 31, 74, 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 31, 74, 40 is 1.
Highest Common Factor of 31,74,40 is 1
Step 1: Since 74 > 31, we apply the division lemma to 74 and 31, to get
74 = 31 x 2 + 12
Step 2: Since the reminder 31 ≠ 0, we apply division lemma to 12 and 31, to get
31 = 12 x 2 + 7
Step 3: We consider the new divisor 12 and the new remainder 7, and apply the division lemma to get
12 = 7 x 1 + 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 31 and 74 is 1
Notice that 1 = HCF(2,1) = HCF(5,2) = HCF(7,5) = HCF(12,7) = HCF(31,12) = HCF(74,31) .
We can take hcf of as 1st numbers and next number as another number to apply in Euclidean lemma
Step 1: Since 40 > 1, we apply the division lemma to 40 and 1, to get
40 = 1 x 40 + 0
The remainder has now become zero, so our procedure stops. Since the divisor at this stage is 1, the HCF of 1 and 40 is 1
Notice that 1 = HCF(40,1) .
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Frequently Asked Questions on HCF of 31, 74, 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 31, 74, 40?
Answer: HCF of 31, 74, 40 is 1 the largest number that divides all the numbers leaving a remainder zero.
3. How to find HCF of 31, 74, 40 using Euclid's Algorithm?
Answer: For arbitrary numbers 31, 74, 40 apply Euclid’s Division Lemma in succession until you obtain a remainder zero. HCF is the remainder in the last but one step.