48 * * There are 10 factors: 1, 2, 3, 4, 6, 8, 12, 16, 24, 48 respectively. Factor means that the quotient of an integer divided by an integer is exactly an integer without a remainder, for example, 48 ÷ 1 = 48. The specific method is: find a factor of an integer, first decompose the integer into prime factors, and then list the number of each factor. For example, an integer has n prime factors, and each prime factor repeats k 1, k2...kn times, then the number of factors = (k1+1) (k2+/kloc-). To find all the factors of 48, first decompose 48 into prime factors, 48 = 2x2x2x2x3, that is, 48 can be decomposed into four prime factors 2, multiplied by 1 prime factor 3, so the number of factors of 48 is (4+1) x (1+1) = The common method is to find the factors of 48: 1, 48, 2, 24, 3, 16, 4, 12, 6, 8, that is, 48 * * has 10 factors.
Brief introduction of factors:
Factor, a mathematical term. If a*b=c(a, B and C are all integers), then we call A and B factors of C. It should be noted that this relationship only holds when the dividend, divisor and quotient are integers and the remainder is zero. On the contrary, we call c a multiple of a and b, and we don't consider 0 when studying factors and multiples. If an integer is divisible by another integer, the former is called a factor of the latter. For example, 1, 3,5 and 15 are all factors of 15. Also known as factor. In primary school mathematics, two positive integers are multiplied, so both numbers are called factors of product, or divisors. In fact, factors are generally defined as integers: let a be an integer and b be a non-zero integer. If there is an integer q, then b is a factor of a, which is recorded as B | A ... but some authors do not require it. For example, if the product of 2 and 6 is 12, then 2 and 6 are factors of 12. 12 is a multiple of 2 and also a multiple of 6. 3X(-9)=-27, 3 and -9 are all factors of -27. -27 is a multiple of 3 and -9. Generally speaking, the integer A is multiplied by the integer B to get the integer C. Both the integer A and the integer B are called factors of the integer C. Conversely, the integer C is a multiple of the integer A and also a multiple of the integer B. ..
Attribute related to factor:
1, divisible: If the integer A is divisible by the non-zero integer B, the quotient is an integer and the remainder is zero, we say that A is divisible by B (or B is divisible by A) and record it as B | A..
2. Prime number (prime number): a natural number with exactly two positive factors. (or defined as a number that is not divisible by other natural numbers except 1 and the integer itself among natural numbers greater than 1).
3. Composite number: There are other positive factors besides 1 and itself.
4. 1 has only a positive factor of 1, so it is neither a prime number nor a composite number.
5. If A is a factor of B and A is a prime number, then A is a prime factor of B ... For example, 2, 3 and 5 are all prime factors of 30. 6 is not a prime number, so it doesn't count. 7 is not a factor of 30, so it is not a prime factor.
6. Two nonzero natural numbers whose common factor is only 1 are called prime numbers.
7. The number of positive factors of 1 nonzero natural number is limited, of which the smallest is1and the largest is itself. The multiples of nonzero natural numbers are infinite.
8. All nonzero integers are factors of 0.
9 and 2 are the smallest prime numbers.
10,4 is the smallest composite number.
Introduction to common factors:
The common factor of two or more integers is called their common factor. The greatest common factor of two or more integers is called their greatest common factor. Inference: 1 is the common factor of any number of integers. Between two nonzero natural numbers with multiple relationships, the smaller number is the greatest common factor of these two numbers.
Brief introduction to short division:
Short division is a method to find the greatest common factor and can also be used to find the least common multiple. The method of finding the greatest common factor of several numbers begins with observation and comparison, that is, first find out the factor of each number, then find out the common factor, and finally find out the greatest common factor in the common factor. After that, the factorization prime factor method is used to decompose the factors of two numbers respectively, and then the operation is carried out. Then it evolved into a short division. The method of short division is to divide the divisor by the prime number divisible by it, and so on until the quotient is a prime number.