Highest Common Factor of 6552, 2219, 16009 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 6552, 2219, 16009 i.e. 7 the largest integer that leaves a remainder zero for all numbers.
HCF of 6552, 2219, 16009 is 7 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 6552, 2219, 16009 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 6552, 2219, 16009 is 7.
HCF(6552, 2219, 16009) = 7
HCF of 6552, 2219, 16009 using Euclid's algorithm
Highest common factor or Highest common divisor (hcd) can be calculated by Euclid's algotithm.
Highest common factor (HCF) of 6552, 2219, 16009 is 7.
Highest Common Factor of 6552,2219,16009 is 7
Step 1: Since 6552 > 2219, we apply the division lemma to 6552 and 2219, to get
6552 = 2219 x 2 + 2114
Step 2: Since the reminder 2219 ≠ 0, we apply division lemma to 2114 and 2219, to get
2219 = 2114 x 1 + 105
Step 3: We consider the new divisor 2114 and the new remainder 105, and apply the division lemma to get
2114 = 105 x 20 + 14
We consider the new divisor 105 and the new remainder 14,and apply the division lemma to get
105 = 14 x 7 + 7
We consider the new divisor 14 and the new remainder 7,and apply the division lemma to get
14 = 7 x 2 + 0
The remainder has now become zero, so our procedure stops. Since the divisor at this stage is 7, the HCF of 6552 and 2219 is 7
Notice that 7 = HCF(14,7) = HCF(105,14) = HCF(2114,105) = HCF(2219,2114) = HCF(6552,2219) .
We can take hcf of as 1st numbers and next number as another number to apply in Euclidean lemma
Step 1: Since 16009 > 7, we apply the division lemma to 16009 and 7, to get
16009 = 7 x 2287 + 0
The remainder has now become zero, so our procedure stops. Since the divisor at this stage is 7, the HCF of 7 and 16009 is 7
Notice that 7 = HCF(16009,7) .
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Frequently Asked Questions on HCF of 6552, 2219, 16009 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 6552, 2219, 16009?
Answer: HCF of 6552, 2219, 16009 is 7 the largest number that divides all the numbers leaving a remainder zero.
3. How to find HCF of 6552, 2219, 16009 using Euclid's Algorithm?
Answer: For arbitrary numbers 6552, 2219, 16009 apply Euclid’s Division Lemma in succession until you obtain a remainder zero. HCF is the remainder in the last but one step.