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These are the integers which can be evenly divided into 105; they can be expressed as either individual factors or as factor pairs. In this case, we present them both ways. This is mathematical decomposition of a particular number. While usually a positive integer, take note of the comments below about negative numbers.
A prime factorization is the result of factoring a number into a set of components which every member is a prime number. This is generally written by showing 105 as a product of its prime factors. For 105, this result would be:105 = 3 x 5 x 7
Yes! 105 is a composite number. It is the product of two positive numbers other than 1 and itself.
No! 105 is not a square number. The square root of this number (10.25) is not an integer.
This number has 8 factors: 1, 3, 5, 7, 15, 21, 35, 105
More specifically, shown as pairs...
(1*105) (3*35) (5*21) (7*15) (15*7) (21*5) (35*3) (105*1)
The greatest common factor of two numbers can be determined by comparing the prime factorization (factorisation in some texts) of the two numbers and taking the highest common prime factor. If there is no common factor, the gcf is 1. This is also referred to as a highest common factor and is part of the common prime factors of two numbers. It is the largest factor (largest number) the two numbers share as a prime factor. The least common factor (smallest number in common) of any pair of integers is 1.
We have a least common multiple calculator here The solution is the lowest common multiple of two numbers.
A factor tree is a graphic representation of the possible factors of a numbers and their sub-factors. It is designed to simplify factorization. It is created by finding the factors of a number, then finding the factors of the factors of a number. The process continues recursively until you've derived a bunch of prime factors, which is the the prime factorization of the original number. In constructing the tree, be sure to remember the second item in a factor pair.
To find the factors of -105, find all the positive factors (see above) and then duplicate them by adding a minus sign before each one (effectively multiplying them by -1). This addresses negative factors. (handling negative integers)
Divisibility refers to a given integer number being divisible for a given divisor. The divisibility rule are a shorthand system to determined what is or isn't divisible. This includes rules about odd number and even number factors. This example is intended to allow the student to estimate the status of a given number without computation.
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