Highest Common Factor of 1994, 3102 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 1994, 3102 i.e. 2 the largest integer that leaves a remainder zero for all numbers.
HCF of 1994, 3102 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 1994, 3102 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 1994, 3102 is 2.
HCF(1994, 3102) = 2
HCF of 1994, 3102 using Euclid's algorithm
Highest common factor or Highest common divisor (hcd) can be calculated by Euclid's algotithm.
Highest common factor (HCF) of 1994, 3102 is 2.
Highest Common Factor of 1994,3102 is 2
Step 1: Since 3102 > 1994, we apply the division lemma to 3102 and 1994, to get
3102 = 1994 x 1 + 1108
Step 2: Since the reminder 1994 ≠ 0, we apply division lemma to 1108 and 1994, to get
1994 = 1108 x 1 + 886
Step 3: We consider the new divisor 1108 and the new remainder 886, and apply the division lemma to get
1108 = 886 x 1 + 222
We consider the new divisor 886 and the new remainder 222,and apply the division lemma to get
886 = 222 x 3 + 220
We consider the new divisor 222 and the new remainder 220,and apply the division lemma to get
222 = 220 x 1 + 2
We consider the new divisor 220 and the new remainder 2,and apply the division lemma to get
220 = 2 x 110 + 0
The remainder has now become zero, so our procedure stops. Since the divisor at this stage is 2, the HCF of 1994 and 3102 is 2
Notice that 2 = HCF(220,2) = HCF(222,220) = HCF(886,222) = HCF(1108,886) = HCF(1994,1108) = HCF(3102,1994) .
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Frequently Asked Questions on HCF of 1994, 3102 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 1994, 3102?
Answer: HCF of 1994, 3102 is 2 the largest number that divides all the numbers leaving a remainder zero.
3. How to find HCF of 1994, 3102 using Euclid's Algorithm?
Answer: For arbitrary numbers 1994, 3102 apply Euclid’s Division Lemma in succession until you obtain a remainder zero. HCF is the remainder in the last but one step.