Highest Common Factor of 52, 84, 14, 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 52, 84, 14, 31 i.e. 1 the largest integer that leaves a remainder zero for all numbers.
HCF of 52, 84, 14, 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 52, 84, 14, 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 52, 84, 14, 31 is 1.
HCF(52, 84, 14, 31) = 1
HCF of 52, 84, 14, 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 52, 84, 14, 31 is 1.
Highest Common Factor of 52,84,14,31 is 1
Step 1: Since 84 > 52, we apply the division lemma to 84 and 52, to get
84 = 52 x 1 + 32
Step 2: Since the reminder 52 ≠ 0, we apply division lemma to 32 and 52, to get
52 = 32 x 1 + 20
Step 3: We consider the new divisor 32 and the new remainder 20, and apply the division lemma to get
32 = 20 x 1 + 12
We consider the new divisor 20 and the new remainder 12,and apply the division lemma to get
20 = 12 x 1 + 8
We consider the new divisor 12 and the new remainder 8,and apply the division lemma to get
12 = 8 x 1 + 4
We consider the new divisor 8 and the new remainder 4,and apply the division lemma to get
8 = 4 x 2 + 0
The remainder has now become zero, so our procedure stops. Since the divisor at this stage is 4, the HCF of 52 and 84 is 4
Notice that 4 = HCF(8,4) = HCF(12,8) = HCF(20,12) = HCF(32,20) = HCF(52,32) = HCF(84,52) .
We can take hcf of as 1st numbers and next number as another number to apply in Euclidean lemma
Step 1: Since 14 > 4, we apply the division lemma to 14 and 4, to get
14 = 4 x 3 + 2
Step 2: Since the reminder 4 ≠ 0, we apply division lemma to 2 and 4, to get
4 = 2 x 2 + 0
The remainder has now become zero, so our procedure stops. Since the divisor at this stage is 2, the HCF of 4 and 14 is 2
Notice that 2 = HCF(4,2) = HCF(14,4) .
We can take hcf of as 1st numbers and next number as another number to apply in Euclidean lemma
Step 1: Since 31 > 2, we apply the division lemma to 31 and 2, to get
31 = 2 x 15 + 1
Step 2: Since the reminder 2 ≠ 0, we apply division lemma to 1 and 2, 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 2 and 31 is 1
Notice that 1 = HCF(2,1) = HCF(31,2) .
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Frequently Asked Questions on HCF of 52, 84, 14, 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 52, 84, 14, 31?
Answer: HCF of 52, 84, 14, 31 is 1 the largest number that divides all the numbers leaving a remainder zero.
3. How to find HCF of 52, 84, 14, 31 using Euclid's Algorithm?
Answer: For arbitrary numbers 52, 84, 14, 31 apply Euclid’s Division Lemma in succession until you obtain a remainder zero. HCF is the remainder in the last but one step.