Highest Common Factor of 1072, 3112 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 1072, 3112 i.e. 8 the largest integer that leaves a remainder zero for all numbers.
HCF of 1072, 3112 is 8 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 1072, 3112 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 1072, 3112 is 8.
HCF(1072, 3112) = 8
HCF of 1072, 3112 using Euclid's algorithm
Highest common factor or Highest common divisor (hcd) can be calculated by Euclid's algotithm.
Highest common factor (HCF) of 1072, 3112 is 8.
Highest Common Factor of 1072,3112 is 8
Step 1: Since 3112 > 1072, we apply the division lemma to 3112 and 1072, to get
3112 = 1072 x 2 + 968
Step 2: Since the reminder 1072 ≠ 0, we apply division lemma to 968 and 1072, to get
1072 = 968 x 1 + 104
Step 3: We consider the new divisor 968 and the new remainder 104, and apply the division lemma to get
968 = 104 x 9 + 32
We consider the new divisor 104 and the new remainder 32,and apply the division lemma to get
104 = 32 x 3 + 8
We consider the new divisor 32 and the new remainder 8,and apply the division lemma to get
32 = 8 x 4 + 0
The remainder has now become zero, so our procedure stops. Since the divisor at this stage is 8, the HCF of 1072 and 3112 is 8
Notice that 8 = HCF(32,8) = HCF(104,32) = HCF(968,104) = HCF(1072,968) = HCF(3112,1072) .
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Frequently Asked Questions on HCF of 1072, 3112 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 1072, 3112?
Answer: HCF of 1072, 3112 is 8 the largest number that divides all the numbers leaving a remainder zero.
3. How to find HCF of 1072, 3112 using Euclid's Algorithm?
Answer: For arbitrary numbers 1072, 3112 apply Euclid’s Division Lemma in succession until you obtain a remainder zero. HCF is the remainder in the last but one step.