Highest Common Factor of 2200, 9216 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 2200, 9216 i.e. 8 the largest integer that leaves a remainder zero for all numbers.
HCF of 2200, 9216 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 2200, 9216 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 2200, 9216 is 8.
HCF(2200, 9216) = 8
HCF of 2200, 9216 using Euclid's algorithm
Highest common factor or Highest common divisor (hcd) can be calculated by Euclid's algotithm.
Highest common factor (HCF) of 2200, 9216 is 8.
Highest Common Factor of 2200,9216 is 8
Step 1: Since 9216 > 2200, we apply the division lemma to 9216 and 2200, to get
9216 = 2200 x 4 + 416
Step 2: Since the reminder 2200 ≠ 0, we apply division lemma to 416 and 2200, to get
2200 = 416 x 5 + 120
Step 3: We consider the new divisor 416 and the new remainder 120, and apply the division lemma to get
416 = 120 x 3 + 56
We consider the new divisor 120 and the new remainder 56,and apply the division lemma to get
120 = 56 x 2 + 8
We consider the new divisor 56 and the new remainder 8,and apply the division lemma to get
56 = 8 x 7 + 0
The remainder has now become zero, so our procedure stops. Since the divisor at this stage is 8, the HCF of 2200 and 9216 is 8
Notice that 8 = HCF(56,8) = HCF(120,56) = HCF(416,120) = HCF(2200,416) = HCF(9216,2200) .
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Frequently Asked Questions on HCF of 2200, 9216 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 2200, 9216?
Answer: HCF of 2200, 9216 is 8 the largest number that divides all the numbers leaving a remainder zero.
3. How to find HCF of 2200, 9216 using Euclid's Algorithm?
Answer: For arbitrary numbers 2200, 9216 apply Euclid’s Division Lemma in succession until you obtain a remainder zero. HCF is the remainder in the last but one step.