Highest Common Factor of 4054, 9970 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 4054, 9970 i.e. 2 the largest integer that leaves a remainder zero for all numbers.
HCF of 4054, 9970 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 4054, 9970 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 4054, 9970 is 2.
HCF(4054, 9970) = 2
HCF of 4054, 9970 using Euclid's algorithm
Highest common factor or Highest common divisor (hcd) can be calculated by Euclid's algotithm.
Highest common factor (HCF) of 4054, 9970 is 2.
Highest Common Factor of 4054,9970 is 2
Step 1: Since 9970 > 4054, we apply the division lemma to 9970 and 4054, to get
9970 = 4054 x 2 + 1862
Step 2: Since the reminder 4054 ≠ 0, we apply division lemma to 1862 and 4054, to get
4054 = 1862 x 2 + 330
Step 3: We consider the new divisor 1862 and the new remainder 330, and apply the division lemma to get
1862 = 330 x 5 + 212
We consider the new divisor 330 and the new remainder 212,and apply the division lemma to get
330 = 212 x 1 + 118
We consider the new divisor 212 and the new remainder 118,and apply the division lemma to get
212 = 118 x 1 + 94
We consider the new divisor 118 and the new remainder 94,and apply the division lemma to get
118 = 94 x 1 + 24
We consider the new divisor 94 and the new remainder 24,and apply the division lemma to get
94 = 24 x 3 + 22
We consider the new divisor 24 and the new remainder 22,and apply the division lemma to get
24 = 22 x 1 + 2
We consider the new divisor 22 and the new remainder 2,and apply the division lemma to get
22 = 2 x 11 + 0
The remainder has now become zero, so our procedure stops. Since the divisor at this stage is 2, the HCF of 4054 and 9970 is 2
Notice that 2 = HCF(22,2) = HCF(24,22) = HCF(94,24) = HCF(118,94) = HCF(212,118) = HCF(330,212) = HCF(1862,330) = HCF(4054,1862) = HCF(9970,4054) .
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Frequently Asked Questions on HCF of 4054, 9970 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 4054, 9970?
Answer: HCF of 4054, 9970 is 2 the largest number that divides all the numbers leaving a remainder zero.
3. How to find HCF of 4054, 9970 using Euclid's Algorithm?
Answer: For arbitrary numbers 4054, 9970 apply Euclid’s Division Lemma in succession until you obtain a remainder zero. HCF is the remainder in the last but one step.