Factors of 612
Factors of 612 are numbers that, when multiplied in pairs give the product as 612. It has total 18 factors of which 612 is the biggest factor and the prime factors of 612 are 2, 3, 17. The sum of all factors of 612 is 1638.
- All Factors of 612: 1, 2, 3, 4, 6, 9, 12, 17, 18, 34, 36, 51, 68, 102, 153, 204, 306 and 612
- Prime Factors of 612: 2, 3, 17
- Prime Factorization of 612: 22 × 32 × 171
- Sum of Factors of 612: 1638
1. | What Are the Factors of 612? |
2. | Factors of 612 by Prime Factorization |
3. | Factors of 612 in Pairs |
4. | FAQs on Factors of 612 |
What are Factors of 612?
Factors of 612 are pairs of those numbers whose products result in 612. These factors are either prime numbers or composite numbers.
How to Find the Factors of 612?
To find the factors of 612, we will have to find the list of numbers that would divide 612 without leaving any remainder.
- 612/17 = 36; therefore, 17 is a factor of 612 and 36 is also a factor of 612.
- 612/68 = 9; therefore, 68 is a factor of 612 and 9 is also a factor of 612.
☛ Also Check:
- Factors of 31 - The factors of 31 are 1, 31
- Factors of 98 - The factors of 98 are 1, 2, 7, 14, 49, 98
- Factors of 70 - The factors of 70 are 1, 2, 5, 7, 10, 14, 35, 70
- Factors of 144 - The factors of 144 are 1, 2, 3, 4, 6, 8, 9, 12, 16, 18, 24, 36, 48, 72, 144
- Factors of 38 - The factors of 38 are 1, 2, 19, 38
Factors of 612 by Prime Factorization
- 612 ÷ 2 = 306
- 306 ÷ 2 = 153
Further dividing 153 by 2 gives a non-zero remainder. So we stop the process and continue dividing the number 153 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 612 can be written as 22 × 32 × 171 where 2, 3, 17 are prime.
Factors of 612 in Pairs
Pair factors of 612 are the pairs of numbers that when multiplied give the product 612. The factors of 612 in pairs are:
- 1 × 612 = (1, 612)
- 2 × 306 = (2, 306)
- 3 × 204 = (3, 204)
- 4 × 153 = (4, 153)
- 6 × 102 = (6, 102)
- 9 × 68 = (9, 68)
- 12 × 51 = (12, 51)
- 17 × 36 = (17, 36)
- 18 × 34 = (18, 34)
Negative pair factors of 612 are:
- -1 × -612 = (-1, -612)
- -2 × -306 = (-2, -306)
- -3 × -204 = (-3, -204)
- -4 × -153 = (-4, -153)
- -6 × -102 = (-6, -102)
- -9 × -68 = (-9, -68)
- -12 × -51 = (-12, -51)
- -17 × -36 = (-17, -36)
- -18 × -34 = (-18, -34)
NOTE: If (a, b) is a pair factor of a number then (b, a) is also a pair factor of that number.
Factors of 612 Solved Examples
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Example 1: How many factors are there for 612?
Solution:
The factors of 612 are too many, therefore if we can find the prime factorization of 612, 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 612 = 22 × 32 × 171
Therefore, the total number of factors are (2 + 1) × (2 + 1) × (1 + 1) = 3 × 3 × 2 = 18 -
Example 2: Find the LCM and Greatest Common Divisor (GCD) of 612 and 117.
Solution:
The factors of 612 are 1, 2, 3, 4, 6, 9, 12, 17, 18, 34, 36, 51, 68, 102, 153, 204, 306, 612 and factors of 117 are 1, 3, 9, 13, 39, 117.
Therefore, the LCM of 612 and 117 is 7956 and Greatest Common Divisor (GCD) of 612 and 117 is 9. -
Example 3: Find if 9, 12, 17, 34, 36, 102, 179 and 204 are factors of 612.
Solution:
When we divide 612 by 179 it leaves a remainder. Therefore, the number 179 is not a factor of 612. All numbers except 179 are factors of 612.
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Example 4: Find the product of all the prime factors of 612.
Solution:
Since, the prime factors of 612 are 2, 3, 17. Therefore, the product of prime factors = 2 × 3 × 17 = 102.
FAQs on Factors of 612
What are the Factors of 612?
The factors of 612 are 1, 2, 3, 4, 6, 9, 12, 17, 18, 34, 36, 51, 68, 102, 153, 204, 306, 612 and its negative factors are -1, -2, -3, -4, -6, -9, -12, -17, -18, -34, -36, -51, -68, -102, -153, -204, -306, -612.
What is the Sum of Factors of 612?
Sum of all factors of 612 = (22 + 1 - 1)/(2 - 1) × (32 + 1 - 1)/(3 - 1) × (171 + 1 - 1)/(17 - 1) = 1638
What are Prime Factors of 612?
The prime factors of 612 are 2, 3, 17.
What is the Greatest Common Factor of 612 and 221?
The factors of 612 and 221 are 1, 2, 3, 4, 6, 9, 12, 17, 18, 34, 36, 51, 68, 102, 153, 204, 306, 612 and 1, 13, 17, 221 respectively.
Common factors of 612 and 221 are [1, 17].
Hence, the GCF of 612 and 221 is 17.
How Many Factors of 478 are also common to the Factors of 612?
Since, the factors of 612 are 1, 2, 3, 4, 6, 9, 12, 17, 18, 34, 36, 51, 68, 102, 153, 204, 306, 612 and the factors of 478 are 1, 2, 239, 478.
Hence, [1, 2] are the common factors of 612 and 478.
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