Highest Common Factor of 474, 2325, 6765 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 474, 2325, 6765 i.e. 3 the largest integer that leaves a remainder zero for all numbers.
HCF of 474, 2325, 6765 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 474, 2325, 6765 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 474, 2325, 6765 is 3.
HCF(474, 2325, 6765) = 3
HCF of 474, 2325, 6765 using Euclid's algorithm
Highest common factor or Highest common divisor (hcd) can be calculated by Euclid's algotithm.
Highest common factor (HCF) of 474, 2325, 6765 is 3.
Highest Common Factor of 474,2325,6765 is 3
Step 1: Since 2325 > 474, we apply the division lemma to 2325 and 474, to get
2325 = 474 x 4 + 429
Step 2: Since the reminder 474 ≠ 0, we apply division lemma to 429 and 474, to get
474 = 429 x 1 + 45
Step 3: We consider the new divisor 429 and the new remainder 45, and apply the division lemma to get
429 = 45 x 9 + 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 474 and 2325 is 3
Notice that 3 = HCF(21,3) = HCF(24,21) = HCF(45,24) = HCF(429,45) = HCF(474,429) = HCF(2325,474) .
We can take hcf of as 1st numbers and next number as another number to apply in Euclidean lemma
Step 1: Since 6765 > 3, we apply the division lemma to 6765 and 3, to get
6765 = 3 x 2255 + 0
The remainder has now become zero, so our procedure stops. Since the divisor at this stage is 3, the HCF of 3 and 6765 is 3
Notice that 3 = HCF(6765,3) .
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Frequently Asked Questions on HCF of 474, 2325, 6765 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 474, 2325, 6765?
Answer: HCF of 474, 2325, 6765 is 3 the largest number that divides all the numbers leaving a remainder zero.
3. How to find HCF of 474, 2325, 6765 using Euclid's Algorithm?
Answer: For arbitrary numbers 474, 2325, 6765 apply Euclid’s Division Lemma in succession until you obtain a remainder zero. HCF is the remainder in the last but one step.