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HCF of 825, 675 and 450
HCF of 825, 675 and 450 is the largest possible number that divides 825, 675 and 450 exactly without any remainder. The factors of 825, 675 and 450 are (1, 3, 5, 11, 15, 25, 33, 55, 75, 165, 275, 825), (1, 3, 5, 9, 15, 25, 27, 45, 75, 135, 225, 675) and (1, 2, 3, 5, 6, 9, 10, 15, 18, 25, 30, 45, 50, 75, 90, 150, 225, 450) respectively. There are 3 commonly used methods to find the HCF of 825, 675 and 450  long division, Euclidean algorithm, and prime factorization.
1.  HCF of 825, 675 and 450 
2.  List of Methods 
3.  Solved Examples 
4.  FAQs 
What is HCF of 825, 675 and 450?
Answer: HCF of 825, 675 and 450 is 75.
Explanation:
The HCF of three nonzero integers, x(825), y(675) and z(450), is the highest positive integer m(75) that divides x(825), y(675) and z(450) without any remainder.
Methods to Find HCF of 825, 675 and 450
The methods to find the HCF of 825, 675 and 450 are explained below.
 Long Division Method
 Listing Common Factors
 Prime Factorization Method
HCF of 825, 675 and 450 by Long Division
HCF of 825, 675 and 450 can be represented as HCF of (HCF of 825, 675) and 450. HCF(825, 675, 450) can be thus calculated by first finding HCF(825, 675) using long division and thereafter using this result with 450 to perform long division again.
 Step 1: Divide 825 (larger number) by 675 (smaller number).
 Step 2: Since the remainder ≠ 0, we will divide the divisor of step 1 (675) by the remainder (150). Repeat this process until the remainder = 0.
⇒ HCF(825, 675) = 75.  Step 3: Now to find the HCF of 75 and 450, we will perform a long division on 450 and 75.
 Step 4: For remainder = 0, divisor = 75 ⇒ HCF(75, 450) = 75
Thus, HCF(825, 675, 450) = HCF(HCF(825, 675), 450) = 75.
HCF of 825, 675 and 450 by Listing Common Factors
 Factors of 825: 1, 3, 5, 11, 15, 25, 33, 55, 75, 165, 275, 825
 Factors of 675: 1, 3, 5, 9, 15, 25, 27, 45, 75, 135, 225, 675
 Factors of 450: 1, 2, 3, 5, 6, 9, 10, 15, 18, 25, 30, 45, 50, 75, 90, 150, 225, 450
There are 6 common factors of 825, 675 and 450, that are 1, 3, 5, 75, 15, and 25. Therefore, the highest common factor of 825, 675 and 450 is 75.
HCF of 825, 675 and 450 by Prime Factorization
Prime factorization of 825, 675 and 450 is (3 × 5 × 5 × 11), (3 × 3 × 3 × 5 × 5) and (2 × 3 × 3 × 5 × 5) respectively. As visible, 825, 675 and 450 have common prime factors. Hence, the HCF of 825, 675 and 450 is 3 × 5 × 5 = 75.
☛ Also Check:
 HCF of 240 and 6552 = 24
 HCF of 2, 4 and 6 = 2
 HCF of 12, 45 and 75 = 3
 HCF of 84 and 144 = 12
 HCF of 150 and 225 = 75
 HCF of 120 and 168 = 24
 HCF of 27 and 36 = 9
HCF of 825, 675 and 450 Examples

Example 1: Verify the relation between the LCM and HCF of 825, 675 and 450.
Solution:
The relation between the LCM and HCF of 825, 675 and 450 is given as, HCF(825, 675, 450) = [(825 × 675 × 450) × LCM(825, 675, 450)]/[LCM(825, 675) × LCM (675, 450) × LCM(825, 450)]
⇒ Prime factorization of 825, 675 and 450: 825 = 3 × 5 × 5 × 11
 675 = 3 × 3 × 3 × 5 × 5
 450 = 2 × 3 × 3 × 5 × 5
∴ LCM of (825, 675), (675, 450), (825, 450), and (825, 675, 450) is 7425, 1350, 4950, and 14850 respectively.
Now, LHS = HCF(825, 675, 450) = 75.
And, RHS = [(825 × 675 × 450) × LCM(825, 675, 450)]/[LCM(825, 675) × LCM (675, 450) × LCM(825, 450)] = [(250593750) × 14850]/[7425 × 1350 × 4950]
LHS = RHS = 75.
Hence verified. 
Example 2: Find the highest number that divides 825, 675, and 450 completely.
Solution:
The highest number that divides 825, 675, and 450 exactly is their highest common factor.
 Factors of 825 = 1, 3, 5, 11, 15, 25, 33, 55, 75, 165, 275, 825
 Factors of 675 = 1, 3, 5, 9, 15, 25, 27, 45, 75, 135, 225, 675
 Factors of 450 = 1, 2, 3, 5, 6, 9, 10, 15, 18, 25, 30, 45, 50, 75, 90, 150, 225, 450
The HCF of 825, 675, and 450 is 75.
∴ The highest number that divides 825, 675, and 450 is 75. 
Example 3: Calculate the HCF of 825, 675, and 450 using LCM of the given numbers.
Solution:
Prime factorization of 825, 675 and 450 is given as,
 825 = 3 × 5 × 5 × 11
 675 = 3 × 3 × 3 × 5 × 5
 450 = 2 × 3 × 3 × 5 × 5
LCM(825, 675) = 7425, LCM(675, 450) = 1350, LCM(450, 825) = 4950, LCM(825, 675, 450) = 14850
⇒ HCF(825, 675, 450) = [(825 × 675 × 450) × LCM(825, 675, 450)]/[LCM(825, 675) × LCM (675, 450) × LCM(450, 825)]
⇒ HCF(825, 675, 450) = (250593750 × 14850)/(7425 × 1350 × 4950)
⇒ HCF(825, 675, 450) = 75.
Therefore, the HCF of 825, 675 and 450 is 75.
FAQs on HCF of 825, 675 and 450
What is the HCF of 825, 675 and 450?
The HCF of 825, 675 and 450 is 75. To calculate the HCF (Highest Common Factor) of 825, 675 and 450, we need to factor each number (factors of 825 = 1, 3, 5, 11, 15, 25, 33, 55, 75, 165, 275, 825; factors of 675 = 1, 3, 5, 9, 15, 25, 27, 45, 75, 135, 225, 675; factors of 450 = 1, 2, 3, 5, 6, 9, 10, 15, 18, 25, 30, 45, 50, 75, 90, 150, 225, 450) and choose the highest factor that exactly divides 825, 675 and 450, i.e., 75.
What is the Relation Between LCM and HCF of 825, 675 and 450?
The following equation can be used to express the relation between LCM (Least Common Multiple) and HCF of 825, 675 and 450, i.e. HCF(825, 675, 450) = [(825 × 675 × 450) × LCM(825, 675, 450)]/[LCM(825, 675) × LCM (675, 450) × LCM(825, 450)].
☛ HCF Calculator
How to Find the HCF of 825, 675 and 450 by Prime Factorization?
To find the HCF of 825, 675 and 450, we will find the prime factorization of given numbers, i.e. 825 = 3 × 5 × 5 × 11; 675 = 3 × 3 × 3 × 5 × 5; 450 = 2 × 3 × 3 × 5 × 5.
⇒ Since 3, 5, 5 are common terms in the prime factorization of 825, 675 and 450. Hence, HCF(825, 675, 450) = 3 × 5 × 5 = 75
☛ Prime Numbers
Which of the following is HCF of 825, 675 and 450? 75, 845, 826, 867, 845, 830, 833, 844
HCF of 825, 675, 450 will be the number that divides 825, 675, and 450 without leaving any remainder. The only number that satisfies the given condition is 75.
What are the Methods to Find HCF of 825, 675 and 450?
There are three commonly used methods to find the HCF of 825, 675 and 450.
 By Prime Factorization
 By Long Division
 By Euclidean Algorithm
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