Highest Common Factor of 7512, 3390, 10016 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 7512, 3390, 10016 i.e. 2 the largest integer that leaves a remainder zero for all numbers.
HCF of 7512, 3390, 10016 is 2 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 7512, 3390, 10016 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 7512, 3390, 10016 is 2.
HCF(7512, 3390, 10016) = 2
HCF of 7512, 3390, 10016 using Euclid's algorithm
Highest common factor or Highest common divisor (hcd) can be calculated by Euclid's algotithm.
Highest common factor (HCF) of 7512, 3390, 10016 is 2.
Highest Common Factor of 7512,3390,10016 is 2
Step 1: Since 7512 > 3390, we apply the division lemma to 7512 and 3390, to get
7512 = 3390 x 2 + 732
Step 2: Since the reminder 3390 ≠ 0, we apply division lemma to 732 and 3390, to get
3390 = 732 x 4 + 462
Step 3: We consider the new divisor 732 and the new remainder 462, and apply the division lemma to get
732 = 462 x 1 + 270
We consider the new divisor 462 and the new remainder 270,and apply the division lemma to get
462 = 270 x 1 + 192
We consider the new divisor 270 and the new remainder 192,and apply the division lemma to get
270 = 192 x 1 + 78
We consider the new divisor 192 and the new remainder 78,and apply the division lemma to get
192 = 78 x 2 + 36
We consider the new divisor 78 and the new remainder 36,and apply the division lemma to get
78 = 36 x 2 + 6
We consider the new divisor 36 and the new remainder 6,and apply the division lemma to get
36 = 6 x 6 + 0
The remainder has now become zero, so our procedure stops. Since the divisor at this stage is 6, the HCF of 7512 and 3390 is 6
Notice that 6 = HCF(36,6) = HCF(78,36) = HCF(192,78) = HCF(270,192) = HCF(462,270) = HCF(732,462) = HCF(3390,732) = HCF(7512,3390) .
We can take hcf of as 1st numbers and next number as another number to apply in Euclidean lemma
Step 1: Since 10016 > 6, we apply the division lemma to 10016 and 6, to get
10016 = 6 x 1669 + 2
Step 2: Since the reminder 6 ≠ 0, we apply division lemma to 2 and 6, to get
6 = 2 x 3 + 0
The remainder has now become zero, so our procedure stops. Since the divisor at this stage is 2, the HCF of 6 and 10016 is 2
Notice that 2 = HCF(6,2) = HCF(10016,6) .
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Frequently Asked Questions on HCF of 7512, 3390, 10016 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 7512, 3390, 10016?
Answer: HCF of 7512, 3390, 10016 is 2 the largest number that divides all the numbers leaving a remainder zero.
3. How to find HCF of 7512, 3390, 10016 using Euclid's Algorithm?
Answer: For arbitrary numbers 7512, 3390, 10016 apply Euclid’s Division Lemma in succession until you obtain a remainder zero. HCF is the remainder in the last but one step.
