Hint:
To solve this problem, we will first find the factors of all three numbers individually. Then we will find out the factors that are common in all three numbers. This will give us the required common factors of all the numbers.
Complete step by step solution:
Here we need to find the common factors of three numbers 5, 15 and 25.
The factor of a number is defined as a number which completely divides that number and gives remainder as zero when divided.
First, we will find the factors of all three numbers individually.
Factors of 5 are 1 and 5.
Factors of the second number i.e. 15 are 1, 3, 5 and 15.
Factors of 25 are 1, 5 and 25.
From these, we can clearly see that 1 and 5 are the factors of all three numbers i.e. 5, 15 and 25.
Hence, the required common factors of 5, 15 and 25 are 1 and 5.
Note:
We might get confused between factors of a number and multiples of a number. A factor is defined as a number that divides the given number completely but the multiple is defined as a number that is completely divided by the given number. Let’s take one example to understand it. Let’s take the number 10. The factors of number 10 are 1, 2, 5 and 10 but the multiples of number 10 are 10, 20, 30, 40, and so on.
Certainly! Analyzing the problem statement provided, it involves identifying the common factors among three numbers: 5, 15, and 25. The methodology suggested is to first ascertain the factors of each number and then determine the factors that are common to all three.
For context, factors are numbers that evenly divide another number without leaving a remainder. Multiples, on the other hand, are values that are products of a given number and any integer.
Let's break down the concepts mentioned in the article and provide some additional information:
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Factors: Factors of a number are integers that can be multiplied together to produce the number. For instance, the factors of 5 are 1 and 5 because 1 * 5 = 5 and these are the only pairs of numbers that, when multiplied, equal 5.
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Finding Factors: To find the factors of a number, you identify the pairs of numbers that multiply together to give the original number. For example, the factors of 15 are 1 15 = 15 and 3 5 = 15. So, the factors of 15 are 1, 3, 5, and 15.
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Common Factors: When dealing with multiple numbers, common factors are the numbers that are factors of all those numbers. In the case of 5, 15, and 25, the factors are 1 and 5 because these numbers divide evenly into all three given numbers.
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Difference between Factors and Multiples: Factors divide a number, while multiples are results of multiplying a number by another integer. For instance, factors of 10 are 1, 2, 5, and 10 because these divide 10 evenly. On the other hand, multiples of 10 are numbers like 20, 30, 40, which are results of multiplying 10 by integers (2 10 = 20, 3 10 = 30, and so on).
Understanding factors and multiples is crucial in mathematics, especially in areas like number theory, algebra, and arithmetic, as they form the foundational elements for solving problems related to divisibility, prime numbers, and more complex mathematical operations.
This approach of finding common factors by first identifying individual factors and then determining the common ones is a fundamental technique used in mathematics to solve problems related to numbers and their properties.
