What is a common factor and what is a common multiple

Common factor, also known as common divisor. It is an integer that is divisible by several integers at the same time. If an integer is a factor of several integers at the same time, the integer is said to be their common factor. Multiples that are common to two or more integers are called their common multiples.

Finding the greatest common factor.

Prime factor decomposition method: decompose the prime factors of each number separately, and then extract all the common prime factors in each number and multiply, and the resulting product is the greatest common divisor of these numbers.

Short division: Short division to find the greatest common divisor, first use the common divisor of these numbers to continuously remove, until all the quotients are co-qualified, and then multiply all the divisors together, and the resulting product is the greatest common divisor of these numbers.

Tossing and dividing: Tossing and dividing is a method of finding the greatest common divisor of two natural numbers, also known as Euclidean's algorithm.

More derogation method: also known as more derogation, is an algorithm for finding the greatest common divisor from the "Nine Chapters of Arithmetic", which was originally designed for reduction, but it is suitable for any occasion where the greatest common divisor needs to be found.

Find the least common multiple.

Decomposing prime factors: first write out the prime factors of these numbers, and the least common multiple is equal to the product of all their prime factors (if there are several prime factors that are the same, compare which of the two numbers has more of the number of prime factors, and multiply more times).

Formula method: Since the product of two numbers is equal to the product of the greatest common divisor and the least common multiple of these two numbers. i.e. (a,b) [a,b]=a b.

So, to find the least common multiple of two numbers, you can first find their greatest common divisor, and then use the above formula to find their least common multiple.

The common factor of two numbers is called the common factor.

For example, 6 and 8, 6 = 2x3, 8 = 2x4, where 2 is the common factor of 6 and 8.

Common multiples are called common multiples.

Such as 6 and 8, a common multiple of two numbers.

6x8=48

4x6=24

3x8=24

Therefore, 24 is the least common multiple of 6 and 8, so 24 is the least common multiple of 6 and 8.

A common factor is an integer that is divisible by several integers at the same time. If an integer is a factor of several integers at the same time, the integer is said to be their common factor. The largest of the factors is called the greatest common factor.

Common multiples are when in two or more natural numbers if they have the same multiple, these multiples are their common multiples. The smallest of the common multiples is called the least common multiple of these integers.

The common divisor is the opposite of a common multiple, that is, it is both a divisor of a and a divisor of b, and the common divisor of 12 and 15 has 1,3, and the greatest common divisor is 3. For example, 30 and 40 have a common divisor of 1, 2, 5, 10, and the greatest common divisor is 10.

The common factor, also known as the common divisor. In the narrative of number theory, if n and d are both integers, and there is an integer c such that n = cd, then d is said to be a factor of n, or n is a multiple of d, denoted as d|n (pronounced d divisible by n).

If d|a and d|b, let's say d is a common factor of a and b. According to Pei Shu's theorem, for each pair of integers a and b, there is a common factor d, such that d=ax+by, where x and y are integers, and each common factor of a and b is divisible by this d. So the absolute value of d is called the greatest common factor.

To find the greatest common factor of several integers, just multiply all of their common prime factors, and the resulting product is their greatest common factor.