The number 112 is evenly divisible by 1, 2, 4, 7, 8, 14, 16, 28, 56, and 112.
A comprehensive guide to the factors of 112
The numbers that can divide 112 without leaving a remainder are known as its factors. Finding these factors reveals fundamental properties about the number, including its prime and composite nature.
Factors and factor pairs
The complete set of factors for 112 can be found by systematically dividing the number by integers. These factors can also be organized into pairs that multiply to equal 112.
Positive factors:1, 2, 4, 7, 8, 14, 16, 28, 56, 112.
Positive factor pairs:
- 1 × 112
- 2 × 56
- 4 × 28
- 7 × 16
- 8 × 14
Negative factors:The negative counterparts of the positive factors also divide 112 evenly.-1, -2, -4, -7, -8, -14, -16, -28, -56, -112.
Prime factorization of 112
Prime factorization is the process of breaking down a composite number into its prime number components. This is a crucial step for understanding all the factors of a number.
The prime factors of 112 are 2 and 7. The prime factorization can be expressed as:112=2×2×2×2×7112 equals 2 cross 2 cross 2 cross 2 cross 7
112=2×2×2×2×7
or in exponential form:112=24×7112 equals 2 to the fourth power cross 7
112=24×7
Using divisibility rules for 112
Divisibility rules offer quick ways to determine if a number is a factor without performing long division.
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112 is divisible by 1 (all integers are).
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It's divisible by 2 because it's an even number, ending in 2.
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It's not divisible by 3, as the sum of its digits (1+1+2=4) is not divisible by 3.
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It's divisible by 4 because its last two digits, 12, are divisible by 4.
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It's not divisible by 6 because it's not divisible by both 2 and 3.
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It's divisible by 7, as 112÷7=16112 divided by 7 equals 16
112÷7=16
.
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It's divisible by 8 because its last three digits, 112, are divisible by 8 (112÷8=14112 divided by 8 equals 14
112÷8=14
).
How to find the factors of 112
Factors can be found through systematic division or using prime factorization. Start with 1 and 112 as factors. Divide by small prime numbers like 2 and 7, finding their corresponding factor pairs (2 and 56, 7 and 16). Continue dividing the quotients (e.g., 56, 28, 14, 7) to find additional factors. The prime factorization (24×72 to the fourth power cross 7
24×7
) can also be used to derive all factors by creating combinations of the prime factors.