Table Of Contents
Last updated on September 25th, 2024
Numbers whose dividend is completely divisible by quotient are its factors. The factor of 49 can neither be a decimal nor a fraction.
1,7 and 49 are the factors of 49.
Negative Factors of 49
These are the negative counterparts of positive factors. The negative factors are -1, -7, -49
Prime Factors of 49
Prime factors are the prime numbers when multiplied, give 49 and 7 is the only prime factor of 49.
Prime Factorization of 49
Process of breaking the given number into its prime factors. Prime Factorization: 7^{2}
An overview of the factors of 49
Positive Factors |
1, 7, 49 |
Negative Factors |
-1, -7, -49 |
Prime Factors |
7 |
Prime Factorization |
7^{2} |
The factors can be found using different methods.
Methods to find the factors of 49 are:
The multiplication method involves finding pairs of numbers that give 49 as their product.
A step-by-step process:
Step 1: Find the possible numbers whose product will give 49.
Step 2: The numbers found should have 49 as the product. These numbers are its factors.
Step 3: Rewrite the particular numbers and pair them.
List of numbers whose product is 49:
1 × 49 = 49
7 × 7 = 49
So the pair of numbers whose product is 49 are (1,49) and (7,7).
The division method helps to find the dividend and quotient as the factors of 49
Step-by-step process:
Step 1: Always start the division with the number 1. Since every number is divisible by 1, the number 1 will always be a factor. Example: 49÷1 = 49
Step 2: Move to the next integer and see if the number gets divided completely. Both divisor and quotient are the factors.
Picture showing the division process:
Here, 1 and 7 are the divisors and 49 is the dividend. 7 and 49 are the quotients. The remainder is zero.
Overview of factors of 49 using the Division Method.
49 ÷ 1 |
49 |
49 ÷ 7 |
7 |
Multiplying prime numbers to get the given number as their product is called prime factors. Prime factorization is the process of breaking down the number into its prime factors.
Prime Factors of 49
Number 49 has only 7 as its prime factor.
To find the prime factor of 49:
Divide 49 with the prime number 7
49÷7 = 7
7÷7 = 1
Prime Factorization of 49
Prime Factorization helps to express the prime factors in their exponential form. Prime Factorization breaks down the prime factors of 49. Prime Factorization of 49 is expressed as 7^{2}
The prime factorization is visually represented using the factor tree. It helps to understand the process easily. In this factor tree, each branch splits into prime factors.
Factor Pairs
Factors of 49 can be written in both positive pairs and negative pairs. The factor pairs are a set of two factors. Their product will be equal to the number given.
Dividend: Number that has to be divided
Quotient: The result we get after dividing a number with another
Odd numbers: Numbers that are not divisible by 2.
Perfect squares: Numbers we get when the same number is multiplied twice.
Greatest Common Factor: The largest integer that divides two or more integers without any remainder
Multiples: The result we get when another number multiplies the given number.