Highest Common Factor of 7431, 846 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 7431, 846 i.e. 3 the largest integer that leaves a remainder zero for all numbers.
HCF of 7431, 846 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 7431, 846 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 7431, 846 is 3.
HCF(7431, 846) = 3
HCF of 7431, 846 using Euclid's algorithm
Highest common factor or Highest common divisor (hcd) can be calculated by Euclid's algotithm.
Highest common factor (HCF) of 7431, 846 is 3.
Highest Common Factor of 7431,846 is 3
Step 1: Since 7431 > 846, we apply the division lemma to 7431 and 846, to get
7431 = 846 x 8 + 663
Step 2: Since the reminder 846 ≠ 0, we apply division lemma to 663 and 846, to get
846 = 663 x 1 + 183
Step 3: We consider the new divisor 663 and the new remainder 183, and apply the division lemma to get
663 = 183 x 3 + 114
We consider the new divisor 183 and the new remainder 114,and apply the division lemma to get
183 = 114 x 1 + 69
We consider the new divisor 114 and the new remainder 69,and apply the division lemma to get
114 = 69 x 1 + 45
We consider the new divisor 69 and the new remainder 45,and apply the division lemma to get
69 = 45 x 1 + 24
We consider the new divisor 45 and the new remainder 24,and apply the division lemma to get
45 = 24 x 1 + 21
We consider the new divisor 24 and the new remainder 21,and apply the division lemma to get
24 = 21 x 1 + 3
We consider the new divisor 21 and the new remainder 3,and apply the division lemma to get
21 = 3 x 7 + 0
The remainder has now become zero, so our procedure stops. Since the divisor at this stage is 3, the HCF of 7431 and 846 is 3
Notice that 3 = HCF(21,3) = HCF(24,21) = HCF(45,24) = HCF(69,45) = HCF(114,69) = HCF(183,114) = HCF(663,183) = HCF(846,663) = HCF(7431,846) .
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Frequently Asked Questions on HCF of 7431, 846 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 7431, 846?
Answer: HCF of 7431, 846 is 3 the largest number that divides all the numbers leaving a remainder zero.
3. How to find HCF of 7431, 846 using Euclid's Algorithm?
Answer: For arbitrary numbers 7431, 846 apply Euclid’s Division Lemma in succession until you obtain a remainder zero. HCF is the remainder in the last but one step.