Highest Common Factor of 345, 7460 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 345, 7460 i.e. 5 the largest integer that leaves a remainder zero for all numbers.
HCF of 345, 7460 is 5 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 345, 7460 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 345, 7460 is 5.
HCF(345, 7460) = 5
HCF of 345, 7460 using Euclid's algorithm
Highest common factor or Highest common divisor (hcd) can be calculated by Euclid's algotithm.
Highest common factor (HCF) of 345, 7460 is 5.
Highest Common Factor of 345,7460 is 5
Step 1: Since 7460 > 345, we apply the division lemma to 7460 and 345, to get
7460 = 345 x 21 + 215
Step 2: Since the reminder 345 ≠ 0, we apply division lemma to 215 and 345, to get
345 = 215 x 1 + 130
Step 3: We consider the new divisor 215 and the new remainder 130, and apply the division lemma to get
215 = 130 x 1 + 85
We consider the new divisor 130 and the new remainder 85,and apply the division lemma to get
130 = 85 x 1 + 45
We consider the new divisor 85 and the new remainder 45,and apply the division lemma to get
85 = 45 x 1 + 40
We consider the new divisor 45 and the new remainder 40,and apply the division lemma to get
45 = 40 x 1 + 5
We consider the new divisor 40 and the new remainder 5,and apply the division lemma to get
40 = 5 x 8 + 0
The remainder has now become zero, so our procedure stops. Since the divisor at this stage is 5, the HCF of 345 and 7460 is 5
Notice that 5 = HCF(40,5) = HCF(45,40) = HCF(85,45) = HCF(130,85) = HCF(215,130) = HCF(345,215) = HCF(7460,345) .
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Frequently Asked Questions on HCF of 345, 7460 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 345, 7460?
Answer: HCF of 345, 7460 is 5 the largest number that divides all the numbers leaving a remainder zero.
3. How to find HCF of 345, 7460 using Euclid's Algorithm?
Answer: For arbitrary numbers 345, 7460 apply Euclid’s Division Lemma in succession until you obtain a remainder zero. HCF is the remainder in the last but one step.