Highest Common Factor of 2160, 7508 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, 7508 i.e. 4 the largest integer that leaves a remainder zero for all numbers.
HCF of 2160, 7508 is 4 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, 7508 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, 7508 is 4.
HCF(2160, 7508) = 4
HCF of 2160, 7508 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, 7508 is 4.
Highest Common Factor of 2160,7508 is 4
Step 1: Since 7508 > 2160, we apply the division lemma to 7508 and 2160, to get
7508 = 2160 x 3 + 1028
Step 2: Since the reminder 2160 ≠ 0, we apply division lemma to 1028 and 2160, to get
2160 = 1028 x 2 + 104
Step 3: We consider the new divisor 1028 and the new remainder 104, and apply the division lemma to get
1028 = 104 x 9 + 92
We consider the new divisor 104 and the new remainder 92,and apply the division lemma to get
104 = 92 x 1 + 12
We consider the new divisor 92 and the new remainder 12,and apply the division lemma to get
92 = 12 x 7 + 8
We consider the new divisor 12 and the new remainder 8,and apply the division lemma to get
12 = 8 x 1 + 4
We consider the new divisor 8 and the new remainder 4,and apply the division lemma to get
8 = 4 x 2 + 0
The remainder has now become zero, so our procedure stops. Since the divisor at this stage is 4, the HCF of 2160 and 7508 is 4
Notice that 4 = HCF(8,4) = HCF(12,8) = HCF(92,12) = HCF(104,92) = HCF(1028,104) = HCF(2160,1028) = HCF(7508,2160) .
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Frequently Asked Questions on HCF of 2160, 7508 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, 7508?
Answer: HCF of 2160, 7508 is 4 the largest number that divides all the numbers leaving a remainder zero.
3. How to find HCF of 2160, 7508 using Euclid's Algorithm?
Answer: For arbitrary numbers 2160, 7508 apply Euclid’s Division Lemma in succession until you obtain a remainder zero. HCF is the remainder in the last but one step.