Highest Common Factor of 735, 57318 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 735, 57318 i.e. 3 the largest integer that leaves a remainder zero for all numbers.
HCF of 735, 57318 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 735, 57318 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 735, 57318 is 3.
HCF(735, 57318) = 3
HCF of 735, 57318 using Euclid's algorithm
Highest common factor or Highest common divisor (hcd) can be calculated by Euclid's algotithm.
Highest common factor (HCF) of 735, 57318 is 3.
Highest Common Factor of 735,57318 is 3
Step 1: Since 57318 > 735, we apply the division lemma to 57318 and 735, to get
57318 = 735 x 77 + 723
Step 2: Since the reminder 735 ≠ 0, we apply division lemma to 723 and 735, to get
735 = 723 x 1 + 12
Step 3: We consider the new divisor 723 and the new remainder 12, and apply the division lemma to get
723 = 12 x 60 + 3
We consider the new divisor 12 and the new remainder 3, and apply the division lemma to get
12 = 3 x 4 + 0
The remainder has now become zero, so our procedure stops. Since the divisor at this stage is 3, the HCF of 735 and 57318 is 3
Notice that 3 = HCF(12,3) = HCF(723,12) = HCF(735,723) = HCF(57318,735) .
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Frequently Asked Questions on HCF of 735, 57318 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 735, 57318?
Answer: HCF of 735, 57318 is 3 the largest number that divides all the numbers leaving a remainder zero.
3. How to find HCF of 735, 57318 using Euclid's Algorithm?
Answer: For arbitrary numbers 735, 57318 apply Euclid’s Division Lemma in succession until you obtain a remainder zero. HCF is the remainder in the last but one step.