Factors of a number are the product of such numbers which completely divide the given number. Factors of a given number can be either positive or negative numbers. By multiplying the factors of a number we get the original number. For example 1, 2, 3, 6 are the factors of 6. On multiplying two or more numbers we get 6. Hence we have 2 x 3 = 6 or 1 x 6 = 6. On this page, we will study the factors of 98 definitions, what are the factors of 98, what is the prime factorization of 98, factor tree of 98, and examples. Factor pairs of the number 98 are the pairs of the whole numbers which could be either positive or negative but not a fraction or decimal number. Factorisation is the common method to find the factors of 98. Let us study the prime factorization of 98.
What are the Factors of a Number?
In elementary school pupils start the subject of mathematics by learning how to count numbers. Various props and activities are performed to practice counting. After the students get comfortable with the digits and can identify their values it is important to understand the values of each number and the quantity they represent. Students learn addition, subtraction, multiplication and division and solve questions based on these basic operations. It helps them to understand and calculate the total amount for any quantity they are provided within their day to day activities. To make it easier there are tables of multiplication that the students practice and by heart. They learn to divide the higher digit numbers by recalling the table they have practised. In the subsequent classes, the problems get advanced such as identifying the multiples of a number and finding out the numbers which can divide a particular number with the remainder zero. These numbers that can perfectly divide a number are known as the factors of that number.
Let's take the example of the number 98 to understand what the factors of a number are.
98 is an even number so it is obvious that the number is divisible by 2. It is not divisible by 3, 4, 5 or 6 so these are not the factors of 98. If we divide the number by 7 then we get the dividend of 14. So both these numbers are the factors of 98. It is again not divisible by 8, 9, 10, 11, 12, or 13. Thus we have found that the 6 factors of 98 are 1, 2, 7, 14, 49, and 98.
What are the Factors of 98 ?
According to the definition of factors of 98 , we know that factors of 98 are all the positive or negative integers which divide the number 98 completely. So let us simply divide the number 98 by every number which completely divides 98 in ascending order till not divides completely
98 \[\div\] 1 = 98
98 \[\div\] 2 = 49
98 \[\div\] 3 = not divides completely
98 \[\div\] 4 = not divides completely
98 \[\div\] 5 = not divides completely
98 \[\div\] 6 = not divides completely
98 \[\div\] 7 = 14
98 \[\div\] 14 = 7
98 \[\div\] 49 = 2
98 \[\div\] 98 = 1
All Factors of 98 can be Listed as Follows
Hence 98 have a total of 6 positive factors and 6 negative factors. All Factor Pairs of 98
All Factor Pairs of 98 are combinations of two factors that when multiplied together give. According to the prime factor definition, we know that the prime factor of a number is the product of all the factors that are prime( a number that divides by itself and only one). Hence we can list the prime factors from the list of factors of Or the other way to find the prime factorization of 98 is by prime factorization or by factor tree.
FAQs on Factors of 98
1. What is HCF?
HCF stands for Highest common factor. When we compare two numbers then we also compare their factors. If there are some factors that are common factors to both the numbers then the highest number among the common factors is identified. This number is termed the highest common factor (HCF) of the two numbers. Similarly, it can be identified for any amount of numbers having some common factors that completely divide the given numbers. To give an example take the numbers 12, 18, and 20. We can find the factors of 12 as 1, 2, 3, 4, 6, and 12. The factors of 18 are 1, 2, 3, 6, 9, and 18. Likewise, the factors of 20 are 1, 2, 4, 5, 10, and 20. If we compare all these numbers we can easily identify that the highest number among all the common factors is 2. Thus 2 is the HCF of 12, 18, and 20.
2. What is LCM?
LCM stands for Lowest Common Multiple. It is identified by finding out all the multiples of the given numbers. After finding all the multiples of the numbers we compare them to find out the common numbers of the present. The smallest number among all the common multiples is termed as lowest common multiple (LCM). To give an example take the numbers 4, 5, and 10. We know that the multiples of 4 are 4, 8, 12, 16, 20, 24 and so on. The multiples of 5 are as follows: 5, 10, 15, 20, 25, and so on. Multiples of 10 are 10, 20, 30, and so on. It is quite evident from the results that 20 is the smallest of all the common multiples that we will obtain from all the common multiples we will get. Thus 20 is the LCM of the 4, 5 and 10.
3. What are prime numbers?
The numbers which are not divisible by any other number than the number 1 and the number itself is called a prime number. In other words, it can be said that the prime numbers have only 2 factors. Some examples of such types of numbers are 2, 3, 5, 7, 11, 13, 17, 19, 23, 29, 31, 37, 41, 43, 47, 53, 59, 61, 67, 71, 73, 79, 83, 89, 97, and so on. There are a total of 25 prime numbers in between 1 to 100.
4. What to do if we can't solve a question containing a problem?
To be good in math students need to practice a lot. For this reason, many questions are provided in the exercises provided at the end of every section or chapter. These questions are in direct relationship with the theory they read in the chapter or it may be a problem based on the concept they learn through the theories. Solving the problems helps to understand the concept much more clearly and remember it. If they can't solve any particular problem then they must reread the theories once again and solve the example questions according to the solution provided.
5. What is the best source to practice questions on multiplication and division?
Practicing mathematics by solving questions is the key to success in this chapter. After solving the questions in the standard textbook followed in the class students must opt for extra questions available. They can find questions in other books published by different publications in the market. To get question sets online they can also visit the website of Vedantu online courses. Many previous year questions and a lot of sample question sets are available here and can be downloaded free of cost after registration.
6. How to Calculate Factors of Large Numbers?
We can calculate factors of large numbers by the trial division method. We first try to divide the number by the smallest number such that it should completely divide the number. The result is again divided by the next number. This step is continued till we get the quotient as 1. At last, we will get all the factors of a given number. For example, let us factorize 100
100 ÷ 2 = 50; first factor is 2
100 ÷ 4 = 25;second factor is 4
100 ÷ 5 = 20;third factor is 5
100 ÷ 10 = 10;fourth factor is 10
100 ÷ 20 = 5;fifth factor is 20
100 ÷ 25 = 4;sixth factor is 25
100 ÷ 50 = 2;seventh factor is 50
100 ÷ 100 = 1;eighth factor is 100
So the factors of 100 are 2, 4, 5, 10, 20, 25, 50 and 100.
7. List the Important Facts of the Factors.
Important Facts of Factors
A factor of any number is its exact divisor i.e it divides the given number exactly.
1 is a common factor of every number.
Every factor of a number is always less than or equal to the original number.
The original number itself is the greatest factor.