Highest Common Factor of 645, 348 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 645, 348 i.e. 3 the largest integer that leaves a remainder zero for all numbers.
HCF of 645, 348 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 645, 348 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 645, 348 is 3.
HCF(645, 348) = 3
HCF of 645, 348 using Euclid's algorithm
Highest common factor or Highest common divisor (hcd) can be calculated by Euclid's algotithm.
Highest common factor (HCF) of 645, 348 is 3.
Highest Common Factor of 645,348 is 3
Step 1: Since 645 > 348, we apply the division lemma to 645 and 348, to get
645 = 348 x 1 + 297
Step 2: Since the reminder 348 ≠ 0, we apply division lemma to 297 and 348, to get
348 = 297 x 1 + 51
Step 3: We consider the new divisor 297 and the new remainder 51, and apply the division lemma to get
297 = 51 x 5 + 42
We consider the new divisor 51 and the new remainder 42,and apply the division lemma to get
51 = 42 x 1 + 9
We consider the new divisor 42 and the new remainder 9,and apply the division lemma to get
42 = 9 x 4 + 6
We consider the new divisor 9 and the new remainder 6,and apply the division lemma to get
9 = 6 x 1 + 3
We consider the new divisor 6 and the new remainder 3,and apply the division lemma to get
6 = 3 x 2 + 0
The remainder has now become zero, so our procedure stops. Since the divisor at this stage is 3, the HCF of 645 and 348 is 3
Notice that 3 = HCF(6,3) = HCF(9,6) = HCF(42,9) = HCF(51,42) = HCF(297,51) = HCF(348,297) = HCF(645,348) .
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Frequently Asked Questions on HCF of 645, 348 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 645, 348?
Answer: HCF of 645, 348 is 3 the largest number that divides all the numbers leaving a remainder zero.
3. How to find HCF of 645, 348 using Euclid's Algorithm?
Answer: For arbitrary numbers 645, 348 apply Euclid’s Division Lemma in succession until you obtain a remainder zero. HCF is the remainder in the last but one step.