Highest Common Factor of 2160, 9752 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 2160, 9752 i.e. 8 the largest integer that leaves a remainder zero for all numbers.
HCF of 2160, 9752 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 2160, 9752 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 2160, 9752 is 8.
HCF(2160, 9752) = 8
HCF of 2160, 9752 using Euclid's algorithm
Highest common factor or Highest common divisor (hcd) can be calculated by Euclid's algotithm.
Highest common factor (HCF) of 2160, 9752 is 8.
Highest Common Factor of 2160,9752 is 8
Step 1: Since 9752 > 2160, we apply the division lemma to 9752 and 2160, to get
9752 = 2160 x 4 + 1112
Step 2: Since the reminder 2160 ≠ 0, we apply division lemma to 1112 and 2160, to get
2160 = 1112 x 1 + 1048
Step 3: We consider the new divisor 1112 and the new remainder 1048, and apply the division lemma to get
1112 = 1048 x 1 + 64
We consider the new divisor 1048 and the new remainder 64,and apply the division lemma to get
1048 = 64 x 16 + 24
We consider the new divisor 64 and the new remainder 24,and apply the division lemma to get
64 = 24 x 2 + 16
We consider the new divisor 24 and the new remainder 16,and apply the division lemma to get
24 = 16 x 1 + 8
We consider the new divisor 16 and the new remainder 8,and apply the division lemma to get
16 = 8 x 2 + 0
The remainder has now become zero, so our procedure stops. Since the divisor at this stage is 8, the HCF of 2160 and 9752 is 8
Notice that 8 = HCF(16,8) = HCF(24,16) = HCF(64,24) = HCF(1048,64) = HCF(1112,1048) = HCF(2160,1112) = HCF(9752,2160) .
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Frequently Asked Questions on HCF of 2160, 9752 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 2160, 9752?
Answer: HCF of 2160, 9752 is 8 the largest number that divides all the numbers leaving a remainder zero.
3. How to find HCF of 2160, 9752 using Euclid's Algorithm?
Answer: For arbitrary numbers 2160, 9752 apply Euclid’s Division Lemma in succession until you obtain a remainder zero. HCF is the remainder in the last but one step.