Factors of 9450
Factors of 9450 are the list of integers that we can split evenly into 9450. There are overall 48 factors of 9450 among which 9450 is the biggest factor and 2, 3, 5, 7 are its prime factors. The Prime Factorization of 9450 is 21 × 33 × 52 × 71.
- All Factors of 9450: 1, 2, 3, 5, 6, 7, 9, 10, 14, 15, 18, 21, 25, 27, 30, 35, 42, 45, 50, 54, 63, 70, 75, 90, 105, 126, 135, 150, 175, 189, 210, 225, 270, 315, 350, 378, 450, 525, 630, 675, 945, 1050, 1350, 1575, 1890, 3150, 4725 and 9450
- Prime Factors of 9450: 2, 3, 5, 7
- Prime Factorization of 9450: 21 × 33 × 52 × 71
- Sum of Factors of 9450: 29760
1. | What Are the Factors of 9450? |
2. | Factors of 9450 by Prime Factorization |
3. | Factors of 9450 in Pairs |
4. | FAQs on Factors of 9450 |
What are Factors of 9450?
Factors of 9450 are pairs of those numbers whose products result in 9450. These factors are either prime numbers or composite numbers.
How to Find the Factors of 9450?
To find the factors of 9450, we will have to find the list of numbers that would divide 9450 without leaving any remainder.
- 9450/135 = 70; therefore, 135 is a factor of 9450 and 70 is also a factor of 9450.
- 9450/1890 = 5; therefore, 1890 is a factor of 9450 and 5 is also a factor of 9450.
☛ Also Check:
- Factors of 48 - The factors of 48 are 1, 2, 3, 4, 6, 8, 12, 16, 24, 48
- Factors of 6 - The factors of 6 are 1, 2, 3, 6
- Factors of 16 - The factors of 16 are 1, 2, 4, 8, 16
- Factors of 11 - The factors of 11 are 1, 11
- Factors of 29 - The factors of 29 are 1, 29
Factors of 9450 by Prime Factorization
- 9450 ÷ 2 = 4725
Further dividing 4725 by 2 gives a non-zero remainder. So we stop the process and continue dividing the number 4725 by the next smallest prime factor. We stop ultimately if the next prime factor doesn't exist or when we can't divide any further.
So, the prime factorization of 9450 can be written as 21 × 33 × 52 × 71 where 2, 3, 5, 7 are prime.
Factors of 9450 in Pairs
Pair factors of 9450 are the pairs of numbers that when multiplied give the product 9450. The factors of 9450 in pairs are:
- 1 × 9450 = (1, 9450)
- 2 × 4725 = (2, 4725)
- 3 × 3150 = (3, 3150)
- 5 × 1890 = (5, 1890)
- 6 × 1575 = (6, 1575)
- 7 × 1350 = (7, 1350)
- 9 × 1050 = (9, 1050)
- 10 × 945 = (10, 945)
- 14 × 675 = (14, 675)
- 15 × 630 = (15, 630)
- 18 × 525 = (18, 525)
- 21 × 450 = (21, 450)
- 25 × 378 = (25, 378)
- 27 × 350 = (27, 350)
- 30 × 315 = (30, 315)
- 35 × 270 = (35, 270)
- 42 × 225 = (42, 225)
- 45 × 210 = (45, 210)
- 50 × 189 = (50, 189)
- 54 × 175 = (54, 175)
- 63 × 150 = (63, 150)
- 70 × 135 = (70, 135)
- 75 × 126 = (75, 126)
- 90 × 105 = (90, 105)
Negative pair factors of 9450 are:
- -1 × -9450 = (-1, -9450)
- -2 × -4725 = (-2, -4725)
- -3 × -3150 = (-3, -3150)
- -5 × -1890 = (-5, -1890)
- -6 × -1575 = (-6, -1575)
- -7 × -1350 = (-7, -1350)
- -9 × -1050 = (-9, -1050)
- -10 × -945 = (-10, -945)
- -14 × -675 = (-14, -675)
- -15 × -630 = (-15, -630)
- -18 × -525 = (-18, -525)
- -21 × -450 = (-21, -450)
- -25 × -378 = (-25, -378)
- -27 × -350 = (-27, -350)
- -30 × -315 = (-30, -315)
- -35 × -270 = (-35, -270)
- -42 × -225 = (-42, -225)
- -45 × -210 = (-45, -210)
- -50 × -189 = (-50, -189)
- -54 × -175 = (-54, -175)
- -63 × -150 = (-63, -150)
- -70 × -135 = (-70, -135)
- -75 × -126 = (-75, -126)
- -90 × -105 = (-90, -105)
NOTE: If (a, b) is a pair factor of a number then (b, a) is also a pair factor of that number.
Factors of 9450 Solved Examples
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Example 1: How many factors are there for 9450?
Solution:
The factors of 9450 are too many, therefore if we can find the prime factorization of 9450, then the total number of factors can be calculated using the formula shown below.
If the prime factorization of the number is ax × by × cz where a, b, c are prime, then the total number of factors can be given by (x + 1)(y + 1)(z + 1).
Prime Factorization of 9450 = 21 × 33 × 52 × 71
Therefore, the total number of factors are (1 + 1) × (3 + 1) × (2 + 1) × (1 + 1) = 2 × 4 × 3 × 2 = 48 -
Example 2: Find the Lowest Common Multiple (LCM) and Greatest Common Divisor (GCD) of 9450 and 1579.
Solution:
The factors of 9450 are 1, 2, 3, 5, 6, 7, 9, 10, 14, 15, 18, 21, 25, 27, 30, 35, 42, 45, 50, 54, 63, 70, 75, 90, 105, 126, 135, 150, 175, 189, 210, 225, 270, 315, 350, 378, 450, 525, 630, 675, 945, 1050, 1350, 1575, 1890, 3150, 4725, 9450 and factors of 1579 are 1, 1579.
Therefore, the Lowest Common Multiple (LCM) of 9450 and 1579 is 14921550 and Greatest Common Divisor (GCD) of 9450 and 1579 is 1. -
Example 3: Find if 2, 10, 42, 90, 105, 270, 1575 and 4302 are factors of 9450.
Solution:
When we divide 9450 by 4302 it leaves a remainder. Therefore, the number 4302 is not a factor of 9450. All numbers except 4302 are factors of 9450.
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Example 4: Find the product of all the prime factors of 9450.
Solution:
Since, the prime factors of 9450 are 2, 3, 5, 7. Therefore, the product of prime factors = 2 × 3 × 5 × 7 = 210.
FAQs on Factors of 9450
What are the Factors of 9450?
The factors of 9450 are 1, 2, 3, 5, 6, 7, 9, 10, 14, 15, 18, 21, 25, 27, 30, 35, 42, 45, 50, 54, 63, 70, 75, 90, 105, 126, 135, 150, 175, 189, 210, 225, 270, 315, 350, 378, 450, 525, 630, 675, 945, 1050, 1350, 1575, 1890, 3150, 4725, 9450 and its negative factors are -1, -2, -3, -5, -6, -7, -9, -10, -14, -15, -18, -21, -25, -27, -30, -35, -42, -45, -50, -54, -63, -70, -75, -90, -105, -126, -135, -150, -175, -189, -210, -225, -270, -315, -350, -378, -450, -525, -630, -675, -945, -1050, -1350, -1575, -1890, -3150, -4725, -9450.
What is the Sum of all the Factors of 9450?
Sum of all factors of 9450 = (21 + 1 - 1)/(2 - 1) × (33 + 1 - 1)/(3 - 1) × (52 + 1 - 1)/(5 - 1) × (71 + 1 - 1)/(7 - 1) = 29760
What are Prime Factors of 9450?
The prime factors of 9450 are 2, 3, 5, 7.
What is the Greatest Common Factor of 9450 and 4447?
The factors of 9450 are 1, 2, 3, 5, 6, 7, 9, 10, 14, 15, 18, 21, 25, 27, 30, 35, 42, 45, 50, 54, 63, 70, 75, 90, 105, 126, 135, 150, 175, 189, 210, 225, 270, 315, 350, 378, 450, 525, 630, 675, 945, 1050, 1350, 1575, 1890, 3150, 4725, 9450 and the factors of 4447 are 1, 4447. 9450 and 4447 have only one common factor which is 1. This implies that 9450 and 4447 are co-prime.
Hence, the Greatest Common Factor (GCF) of 9450 and 4447 is 1.
How Many Factors of 7946 are also common to the Factors of 9450?
Since, the factors of 9450 are 1, 2, 3, 5, 6, 7, 9, 10, 14, 15, 18, 21, 25, 27, 30, 35, 42, 45, 50, 54, 63, 70, 75, 90, 105, 126, 135, 150, 175, 189, 210, 225, 270, 315, 350, 378, 450, 525, 630, 675, 945, 1050, 1350, 1575, 1890, 3150, 4725, 9450 and the factors of 7946 are 1, 2, 29, 58, 137, 274, 3973, 7946.
Hence, [1, 2] are the common factors of 9450 and 7946.
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