Highest Common Factor of 9006, 759 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 9006, 759 i.e. 3 the largest integer that leaves a remainder zero for all numbers.
HCF of 9006, 759 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 9006, 759 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 9006, 759 is 3.
HCF(9006, 759) = 3
HCF of 9006, 759 using Euclid's algorithm
Highest common factor or Highest common divisor (hcd) can be calculated by Euclid's algotithm.
Highest common factor (HCF) of 9006, 759 is 3.
Highest Common Factor of 9006,759 is 3
Step 1: Since 9006 > 759, we apply the division lemma to 9006 and 759, to get
9006 = 759 x 11 + 657
Step 2: Since the reminder 759 ≠ 0, we apply division lemma to 657 and 759, to get
759 = 657 x 1 + 102
Step 3: We consider the new divisor 657 and the new remainder 102, and apply the division lemma to get
657 = 102 x 6 + 45
We consider the new divisor 102 and the new remainder 45,and apply the division lemma to get
102 = 45 x 2 + 12
We consider the new divisor 45 and the new remainder 12,and apply the division lemma to get
45 = 12 x 3 + 9
We consider the new divisor 12 and the new remainder 9,and apply the division lemma to get
12 = 9 x 1 + 3
We consider the new divisor 9 and the new remainder 3,and apply the division lemma to get
9 = 3 x 3 + 0
The remainder has now become zero, so our procedure stops. Since the divisor at this stage is 3, the HCF of 9006 and 759 is 3
Notice that 3 = HCF(9,3) = HCF(12,9) = HCF(45,12) = HCF(102,45) = HCF(657,102) = HCF(759,657) = HCF(9006,759) .
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Frequently Asked Questions on HCF of 9006, 759 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 9006, 759?
Answer: HCF of 9006, 759 is 3 the largest number that divides all the numbers leaving a remainder zero.
3. How to find HCF of 9006, 759 using Euclid's Algorithm?
Answer: For arbitrary numbers 9006, 759 apply Euclid’s Division Lemma in succession until you obtain a remainder zero. HCF is the remainder in the last but one step.