Highest Common Factor of 2988, 7128 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 2988, 7128 i.e. 36 the largest integer that leaves a remainder zero for all numbers.
HCF of 2988, 7128 is 36 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 2988, 7128 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 2988, 7128 is 36.
HCF(2988, 7128) = 36
HCF of 2988, 7128 using Euclid's algorithm
Highest common factor or Highest common divisor (hcd) can be calculated by Euclid's algotithm.
Highest common factor (HCF) of 2988, 7128 is 36.
Highest Common Factor of 2988,7128 is 36
Step 1: Since 7128 > 2988, we apply the division lemma to 7128 and 2988, to get
7128 = 2988 x 2 + 1152
Step 2: Since the reminder 2988 ≠ 0, we apply division lemma to 1152 and 2988, to get
2988 = 1152 x 2 + 684
Step 3: We consider the new divisor 1152 and the new remainder 684, and apply the division lemma to get
1152 = 684 x 1 + 468
We consider the new divisor 684 and the new remainder 468,and apply the division lemma to get
684 = 468 x 1 + 216
We consider the new divisor 468 and the new remainder 216,and apply the division lemma to get
468 = 216 x 2 + 36
We consider the new divisor 216 and the new remainder 36,and apply the division lemma to get
216 = 36 x 6 + 0
The remainder has now become zero, so our procedure stops. Since the divisor at this stage is 36, the HCF of 2988 and 7128 is 36
Notice that 36 = HCF(216,36) = HCF(468,216) = HCF(684,468) = HCF(1152,684) = HCF(2988,1152) = HCF(7128,2988) .
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Frequently Asked Questions on HCF of 2988, 7128 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 2988, 7128?
Answer: HCF of 2988, 7128 is 36 the largest number that divides all the numbers leaving a remainder zero.
3. How to find HCF of 2988, 7128 using Euclid's Algorithm?
Answer: For arbitrary numbers 2988, 7128 apply Euclid’s Division Lemma in succession until you obtain a remainder zero. HCF is the remainder in the last but one step.