Highest Common Factor of 72, 58, 420, 112 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 72, 58, 420, 112 i.e. 2 the largest integer that leaves a remainder zero for all numbers.
HCF of 72, 58, 420, 112 is 2 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 72, 58, 420, 112 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 72, 58, 420, 112 is 2.
HCF(72, 58, 420, 112) = 2
HCF of 72, 58, 420, 112 using Euclid's algorithm
Highest common factor or Highest common divisor (hcd) can be calculated by Euclid's algotithm.
Highest common factor (HCF) of 72, 58, 420, 112 is 2.
Highest Common Factor of 72,58,420,112 is 2
Step 1: Since 72 > 58, we apply the division lemma to 72 and 58, to get
72 = 58 x 1 + 14
Step 2: Since the reminder 58 ≠ 0, we apply division lemma to 14 and 58, to get
58 = 14 x 4 + 2
Step 3: We consider the new divisor 14 and the new remainder 2, and apply the division lemma to get
14 = 2 x 7 + 0
The remainder has now become zero, so our procedure stops. Since the divisor at this stage is 2, the HCF of 72 and 58 is 2
Notice that 2 = HCF(14,2) = HCF(58,14) = HCF(72,58) .
We can take hcf of as 1st numbers and next number as another number to apply in Euclidean lemma
Step 1: Since 420 > 2, we apply the division lemma to 420 and 2, to get
420 = 2 x 210 + 0
The remainder has now become zero, so our procedure stops. Since the divisor at this stage is 2, the HCF of 2 and 420 is 2
Notice that 2 = HCF(420,2) .
We can take hcf of as 1st numbers and next number as another number to apply in Euclidean lemma
Step 1: Since 112 > 2, we apply the division lemma to 112 and 2, to get
112 = 2 x 56 + 0
The remainder has now become zero, so our procedure stops. Since the divisor at this stage is 2, the HCF of 2 and 112 is 2
Notice that 2 = HCF(112,2) .
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Frequently Asked Questions on HCF of 72, 58, 420, 112 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 72, 58, 420, 112?
Answer: HCF of 72, 58, 420, 112 is 2 the largest number that divides all the numbers leaving a remainder zero.
3. How to find HCF of 72, 58, 420, 112 using Euclid's Algorithm?
Answer: For arbitrary numbers 72, 58, 420, 112 apply Euclid’s Division Lemma in succession until you obtain a remainder zero. HCF is the remainder in the last but one step.