Hello friends today in this session of mathematics we are going to learn about some of the topics related to factors and exponents. This article will include the some of the topics of V grade of maharashtra state education board like common factors, prime factors, and exponents.
Now talking about the common factors for the grade V, we should have a understanding of the factors that what they are, So, the factors are the numbers that on multiplying positive and negative numbers produces another number. Each number has at least two factors. For example 12 = 2*6 so factors of 12 are 2 and 6. Now common factors are the numbers which are common in two or more numbers. In math question we use the greatest common factor (GCF). The GCF is the number which is shared in both of the numbers. The greatest common factor is the number which is largest in the common factors. For example the GCF of the 24, 36, and 48 is 12 and GCF of 15, 30, and 105 is 15.
Factors of 24 = 1, 2, 3, 4, 6, 8, and 12
Factors of 36 = 1, 2, 3, 4, 6, 12, and 18
Factors of 48 = 1, 2, 3, 4, 6, 12, and 24 and for more gcf examples refer this link
Now talking about prime factors. The prime factors are the type of factors that are also prime in nature. These also on multiplication produce the original number. For the example the prime factor of 12:
12 = 2 * 6
= 2 * 2 * 3
= 22 * 3
So, prime factors of 12 are 2 and 3. The number 12 can also be written as 2 * 6 but 6 is not a prime number so it is not a prime factor for the number 12. Another example would be 15 which have the prime factor as 3 and 5 because both of the numbers are prime in nature. To find the prime factor we perform the prime factorization of the number. Prime factorization of a number is done for the purpose to find the prime number. For example performing the factorization on some of the numbers to find prime factors as:
12 = 2 × 2 × 3 (prime factors 2, 3)
15 = 3 * 5 (prime factors 3, 5)
24 = 2 * 2 * 2 * 3 (prime factors 2, 3)
147 = 3 * 7 * 7 (prime factors 3, 7)
The prime factors of an integer are numbers which divides that integer with no remainder and didn’t leave any remainder. The term exponent can be understood here by some of the definition that the exponents are the type of shorthand’s that comes for the replacement of the repetition of several numbers in the factorizations.
Just for example we consider some of the numbers:
24 = 2 * 2 * 2 * 3
This can be written in the form of exponent as 23 * 3. Here 3 in the power of two is the exponent. The exponent shows that how many times the number is multiplied with a itself. The number that is being multiplied, as 2 in this example, is called as “base”. We also call it “rising to the power” where exponent is the power. In the example 48 = 24 * 3, 2 is base and 4 is exponent on the 2. It is pronounced as “2 to the power 4” or “two to the four.
This is all about the Factors and Exponents and if anybody wants to know about Factorizing a Trinomial by splitting the middle terms and also Mathematical Reasoning then they can refer to Internet and text books for understanding it more precisely.
Now talking about the common factors for the grade V, we should have a understanding of the factors that what they are, So, the factors are the numbers that on multiplying positive and negative numbers produces another number. Each number has at least two factors. For example 12 = 2*6 so factors of 12 are 2 and 6. Now common factors are the numbers which are common in two or more numbers. In math question we use the greatest common factor (GCF). The GCF is the number which is shared in both of the numbers. The greatest common factor is the number which is largest in the common factors. For example the GCF of the 24, 36, and 48 is 12 and GCF of 15, 30, and 105 is 15.
Factors of 24 = 1, 2, 3, 4, 6, 8, and 12
Factors of 36 = 1, 2, 3, 4, 6, 12, and 18
Factors of 48 = 1, 2, 3, 4, 6, 12, and 24 and for more gcf examples refer this link
Now talking about prime factors. The prime factors are the type of factors that are also prime in nature. These also on multiplication produce the original number. For the example the prime factor of 12:
12 = 2 * 6
= 2 * 2 * 3
= 22 * 3
So, prime factors of 12 are 2 and 3. The number 12 can also be written as 2 * 6 but 6 is not a prime number so it is not a prime factor for the number 12. Another example would be 15 which have the prime factor as 3 and 5 because both of the numbers are prime in nature. To find the prime factor we perform the prime factorization of the number. Prime factorization of a number is done for the purpose to find the prime number. For example performing the factorization on some of the numbers to find prime factors as:
12 = 2 × 2 × 3 (prime factors 2, 3)
15 = 3 * 5 (prime factors 3, 5)
24 = 2 * 2 * 2 * 3 (prime factors 2, 3)
147 = 3 * 7 * 7 (prime factors 3, 7)
The prime factors of an integer are numbers which divides that integer with no remainder and didn’t leave any remainder. The term exponent can be understood here by some of the definition that the exponents are the type of shorthand’s that comes for the replacement of the repetition of several numbers in the factorizations.
Just for example we consider some of the numbers:
24 = 2 * 2 * 2 * 3
This can be written in the form of exponent as 23 * 3. Here 3 in the power of two is the exponent. The exponent shows that how many times the number is multiplied with a itself. The number that is being multiplied, as 2 in this example, is called as “base”. We also call it “rising to the power” where exponent is the power. In the example 48 = 24 * 3, 2 is base and 4 is exponent on the 2. It is pronounced as “2 to the power 4” or “two to the four.
This is all about the Factors and Exponents and if anybody wants to know about Factorizing a Trinomial by splitting the middle terms and also Mathematical Reasoning then they can refer to Internet and text books for understanding it more precisely.
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