Highest Common Factor of 675, 1575, 7314 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 675, 1575, 7314 i.e. 3 the largest integer that leaves a remainder zero for all numbers.
HCF of 675, 1575, 7314 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 675, 1575, 7314 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 675, 1575, 7314 is 3.
HCF(675, 1575, 7314) = 3
HCF of 675, 1575, 7314 using Euclid's algorithm
Highest common factor or Highest common divisor (hcd) can be calculated by Euclid's algotithm.
Highest common factor (HCF) of 675, 1575, 7314 is 3.
Highest Common Factor of 675,1575,7314 is 3
Step 1: Since 1575 > 675, we apply the division lemma to 1575 and 675, to get
1575 = 675 x 2 + 225
Step 2: Since the reminder 675 ≠ 0, we apply division lemma to 225 and 675, to get
675 = 225 x 3 + 0
The remainder has now become zero, so our procedure stops. Since the divisor at this stage is 225, the HCF of 675 and 1575 is 225
Notice that 225 = HCF(675,225) = HCF(1575,675) .
We can take hcf of as 1st numbers and next number as another number to apply in Euclidean lemma
Step 1: Since 7314 > 225, we apply the division lemma to 7314 and 225, to get
7314 = 225 x 32 + 114
Step 2: Since the reminder 225 ≠ 0, we apply division lemma to 114 and 225, to get
225 = 114 x 1 + 111
Step 3: We consider the new divisor 114 and the new remainder 111, and apply the division lemma to get
114 = 111 x 1 + 3
We consider the new divisor 111 and the new remainder 3, and apply the division lemma to get
111 = 3 x 37 + 0
The remainder has now become zero, so our procedure stops. Since the divisor at this stage is 3, the HCF of 225 and 7314 is 3
Notice that 3 = HCF(111,3) = HCF(114,111) = HCF(225,114) = HCF(7314,225) .
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Frequently Asked Questions on HCF of 675, 1575, 7314 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 675, 1575, 7314?
Answer: HCF of 675, 1575, 7314 is 3 the largest number that divides all the numbers leaving a remainder zero.
3. How to find HCF of 675, 1575, 7314 using Euclid's Algorithm?
Answer: For arbitrary numbers 675, 1575, 7314 apply Euclid’s Division Lemma in succession until you obtain a remainder zero. HCF is the remainder in the last but one step.