Highest Common Factor of 846, 51075 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, 51075 i.e. 9 the largest integer that leaves a remainder zero for all numbers.
HCF of 846, 51075 is 9 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, 51075 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, 51075 is 9.
HCF(846, 51075) = 9
HCF of 846, 51075 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, 51075 is 9.
Highest Common Factor of 846,51075 is 9
Step 1: Since 51075 > 846, we apply the division lemma to 51075 and 846, to get
51075 = 846 x 60 + 315
Step 2: Since the reminder 846 ≠ 0, we apply division lemma to 315 and 846, to get
846 = 315 x 2 + 216
Step 3: We consider the new divisor 315 and the new remainder 216, and apply the division lemma to get
315 = 216 x 1 + 99
We consider the new divisor 216 and the new remainder 99,and apply the division lemma to get
216 = 99 x 2 + 18
We consider the new divisor 99 and the new remainder 18,and apply the division lemma to get
99 = 18 x 5 + 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 51075 is 9
Notice that 9 = HCF(18,9) = HCF(99,18) = HCF(216,99) = HCF(315,216) = HCF(846,315) = HCF(51075,846) .
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Frequently Asked Questions on HCF of 846, 51075 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, 51075?
Answer: HCF of 846, 51075 is 9 the largest number that divides all the numbers leaving a remainder zero.
3. How to find HCF of 846, 51075 using Euclid's Algorithm?
Answer: For arbitrary numbers 846, 51075 apply Euclid’s Division Lemma in succession until you obtain a remainder zero. HCF is the remainder in the last but one step.