Highest Common Factor of 5973, 3108 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 5973, 3108 i.e. 3 the largest integer that leaves a remainder zero for all numbers.
HCF of 5973, 3108 is 3 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 5973, 3108 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 5973, 3108 is 3.
HCF(5973, 3108) = 3
HCF of 5973, 3108 using Euclid's algorithm
Highest common factor or Highest common divisor (hcd) can be calculated by Euclid's algotithm.
Highest common factor (HCF) of 5973, 3108 is 3.
Highest Common Factor of 5973,3108 is 3
Step 1: Since 5973 > 3108, we apply the division lemma to 5973 and 3108, to get
5973 = 3108 x 1 + 2865
Step 2: Since the reminder 3108 ≠ 0, we apply division lemma to 2865 and 3108, to get
3108 = 2865 x 1 + 243
Step 3: We consider the new divisor 2865 and the new remainder 243, and apply the division lemma to get
2865 = 243 x 11 + 192
We consider the new divisor 243 and the new remainder 192,and apply the division lemma to get
243 = 192 x 1 + 51
We consider the new divisor 192 and the new remainder 51,and apply the division lemma to get
192 = 51 x 3 + 39
We consider the new divisor 51 and the new remainder 39,and apply the division lemma to get
51 = 39 x 1 + 12
We consider the new divisor 39 and the new remainder 12,and apply the division lemma to get
39 = 12 x 3 + 3
We consider the new divisor 12 and the new remainder 3,and apply the division lemma to get
12 = 3 x 4 + 0
The remainder has now become zero, so our procedure stops. Since the divisor at this stage is 3, the HCF of 5973 and 3108 is 3
Notice that 3 = HCF(12,3) = HCF(39,12) = HCF(51,39) = HCF(192,51) = HCF(243,192) = HCF(2865,243) = HCF(3108,2865) = HCF(5973,3108) .
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Frequently Asked Questions on HCF of 5973, 3108 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 5973, 3108?
Answer: HCF of 5973, 3108 is 3 the largest number that divides all the numbers leaving a remainder zero.
3. How to find HCF of 5973, 3108 using Euclid's Algorithm?
Answer: For arbitrary numbers 5973, 3108 apply Euclid’s Division Lemma in succession until you obtain a remainder zero. HCF is the remainder in the last but one step.