Highest Common Factor of 720, 996, 41 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 720, 996, 41 i.e. 1 the largest integer that leaves a remainder zero for all numbers.
HCF of 720, 996, 41 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 720, 996, 41 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 720, 996, 41 is 1.
HCF(720, 996, 41) = 1
HCF of 720, 996, 41 using Euclid's algorithm
Highest common factor or Highest common divisor (hcd) can be calculated by Euclid's algotithm.
Highest common factor (HCF) of 720, 996, 41 is 1.
Highest Common Factor of 720,996,41 is 1
Step 1: Since 996 > 720, we apply the division lemma to 996 and 720, to get
996 = 720 x 1 + 276
Step 2: Since the reminder 720 ≠ 0, we apply division lemma to 276 and 720, to get
720 = 276 x 2 + 168
Step 3: We consider the new divisor 276 and the new remainder 168, and apply the division lemma to get
276 = 168 x 1 + 108
We consider the new divisor 168 and the new remainder 108,and apply the division lemma to get
168 = 108 x 1 + 60
We consider the new divisor 108 and the new remainder 60,and apply the division lemma to get
108 = 60 x 1 + 48
We consider the new divisor 60 and the new remainder 48,and apply the division lemma to get
60 = 48 x 1 + 12
We consider the new divisor 48 and the new remainder 12,and apply the division lemma to get
48 = 12 x 4 + 0
The remainder has now become zero, so our procedure stops. Since the divisor at this stage is 12, the HCF of 720 and 996 is 12
Notice that 12 = HCF(48,12) = HCF(60,48) = HCF(108,60) = HCF(168,108) = HCF(276,168) = HCF(720,276) = HCF(996,720) .
We can take hcf of as 1st numbers and next number as another number to apply in Euclidean lemma
Step 1: Since 41 > 12, we apply the division lemma to 41 and 12, to get
41 = 12 x 3 + 5
Step 2: Since the reminder 12 ≠ 0, we apply division lemma to 5 and 12, to get
12 = 5 x 2 + 2
Step 3: 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 12 and 41 is 1
Notice that 1 = HCF(2,1) = HCF(5,2) = HCF(12,5) = HCF(41,12) .
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Frequently Asked Questions on HCF of 720, 996, 41 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 720, 996, 41?
Answer: HCF of 720, 996, 41 is 1 the largest number that divides all the numbers leaving a remainder zero.
3. How to find HCF of 720, 996, 41 using Euclid's Algorithm?
Answer: For arbitrary numbers 720, 996, 41 apply Euclid’s Division Lemma in succession until you obtain a remainder zero. HCF is the remainder in the last but one step.