Highest Common Factor of 846, 7281, 5952 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 846, 7281, 5952 i.e. 3 the largest integer that leaves a remainder zero for all numbers.
HCF of 846, 7281, 5952 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 846, 7281, 5952 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 846, 7281, 5952 is 3.
HCF(846, 7281, 5952) = 3
HCF of 846, 7281, 5952 using Euclid's algorithm
Highest common factor or Highest common divisor (hcd) can be calculated by Euclid's algotithm.
Highest common factor (HCF) of 846, 7281, 5952 is 3.
Highest Common Factor of 846,7281,5952 is 3
Step 1: Since 7281 > 846, we apply the division lemma to 7281 and 846, to get
7281 = 846 x 8 + 513
Step 2: Since the reminder 846 ≠ 0, we apply division lemma to 513 and 846, to get
846 = 513 x 1 + 333
Step 3: We consider the new divisor 513 and the new remainder 333, and apply the division lemma to get
513 = 333 x 1 + 180
We consider the new divisor 333 and the new remainder 180,and apply the division lemma to get
333 = 180 x 1 + 153
We consider the new divisor 180 and the new remainder 153,and apply the division lemma to get
180 = 153 x 1 + 27
We consider the new divisor 153 and the new remainder 27,and apply the division lemma to get
153 = 27 x 5 + 18
We consider the new divisor 27 and the new remainder 18,and apply the division lemma to get
27 = 18 x 1 + 9
We consider the new divisor 18 and the new remainder 9,and apply the division lemma to get
18 = 9 x 2 + 0
The remainder has now become zero, so our procedure stops. Since the divisor at this stage is 9, the HCF of 846 and 7281 is 9
Notice that 9 = HCF(18,9) = HCF(27,18) = HCF(153,27) = HCF(180,153) = HCF(333,180) = HCF(513,333) = HCF(846,513) = HCF(7281,846) .
We can take hcf of as 1st numbers and next number as another number to apply in Euclidean lemma
Step 1: Since 5952 > 9, we apply the division lemma to 5952 and 9, to get
5952 = 9 x 661 + 3
Step 2: Since the reminder 9 ≠ 0, we apply division lemma to 3 and 9, 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 9 and 5952 is 3
Notice that 3 = HCF(9,3) = HCF(5952,9) .
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Frequently Asked Questions on HCF of 846, 7281, 5952 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 846, 7281, 5952?
Answer: HCF of 846, 7281, 5952 is 3 the largest number that divides all the numbers leaving a remainder zero.
3. How to find HCF of 846, 7281, 5952 using Euclid's Algorithm?
Answer: For arbitrary numbers 846, 7281, 5952 apply Euclid’s Division Lemma in succession until you obtain a remainder zero. HCF is the remainder in the last but one step.