Highest Common Factor of 53, 74, 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 53, 74, 31 i.e. 1 the largest integer that leaves a remainder zero for all numbers.
HCF of 53, 74, 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 53, 74, 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 53, 74, 31 is 1.
HCF(53, 74, 31) = 1
HCF of 53, 74, 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 53, 74, 31 is 1.
Highest Common Factor of 53,74,31 is 1
Step 1: Since 74 > 53, we apply the division lemma to 74 and 53, to get
74 = 53 x 1 + 21
Step 2: Since the reminder 53 ≠ 0, we apply division lemma to 21 and 53, to get
53 = 21 x 2 + 11
Step 3: We consider the new divisor 21 and the new remainder 11, and apply the division lemma to get
21 = 11 x 1 + 10
We consider the new divisor 11 and the new remainder 10,and apply the division lemma to get
11 = 10 x 1 + 1
We consider the new divisor 10 and the new remainder 1,and apply the division lemma to get
10 = 1 x 10 + 0
The remainder has now become zero, so our procedure stops. Since the divisor at this stage is 1, the HCF of 53 and 74 is 1
Notice that 1 = HCF(10,1) = HCF(11,10) = HCF(21,11) = HCF(53,21) = HCF(74,53) .
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 53, 74, 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 53, 74, 31?
Answer: HCF of 53, 74, 31 is 1 the largest number that divides all the numbers leaving a remainder zero.
3. How to find HCF of 53, 74, 31 using Euclid's Algorithm?
Answer: For arbitrary numbers 53, 74, 31 apply Euclid’s Division Lemma in succession until you obtain a remainder zero. HCF is the remainder in the last but one step.