Highest Common Factor of 9972, 5007 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 9972, 5007 i.e. 3 the largest integer that leaves a remainder zero for all numbers.
HCF of 9972, 5007 is 3 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 9972, 5007 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 9972, 5007 is 3.
HCF(9972, 5007) = 3
HCF of 9972, 5007 using Euclid's algorithm
Highest common factor or Highest common divisor (hcd) can be calculated by Euclid's algotithm.
Highest common factor (HCF) of 9972, 5007 is 3.
Highest Common Factor of 9972,5007 is 3
Step 1: Since 9972 > 5007, we apply the division lemma to 9972 and 5007, to get
9972 = 5007 x 1 + 4965
Step 2: Since the reminder 5007 ≠ 0, we apply division lemma to 4965 and 5007, to get
5007 = 4965 x 1 + 42
Step 3: We consider the new divisor 4965 and the new remainder 42, and apply the division lemma to get
4965 = 42 x 118 + 9
We consider the new divisor 42 and the new remainder 9,and apply the division lemma to get
42 = 9 x 4 + 6
We consider the new divisor 9 and the new remainder 6,and apply the division lemma to get
9 = 6 x 1 + 3
We consider the new divisor 6 and the new remainder 3,and apply the division lemma to get
6 = 3 x 2 + 0
The remainder has now become zero, so our procedure stops. Since the divisor at this stage is 3, the HCF of 9972 and 5007 is 3
Notice that 3 = HCF(6,3) = HCF(9,6) = HCF(42,9) = HCF(4965,42) = HCF(5007,4965) = HCF(9972,5007) .
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Frequently Asked Questions on HCF of 9972, 5007 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 9972, 5007?
Answer: HCF of 9972, 5007 is 3 the largest number that divides all the numbers leaving a remainder zero.
3. How to find HCF of 9972, 5007 using Euclid's Algorithm?
Answer: For arbitrary numbers 9972, 5007 apply Euclid’s Division Lemma in succession until you obtain a remainder zero. HCF is the remainder in the last but one step.