How do you find the number of factors of a given number?

We can find the factors of a number by dividing the number by all possible divisors . To find all the factors of a number n using the division method, divide the number by all the natural numbers less than n. Identify the numbers that completely divide the given number.

How many odd factors are there in 1260?

∴ The total number of odd factors of 1260 is 12 -> Candidates can check their venue, date, and shift for which the exam will be conducted.

How many factors of 1260 do not end with a zero?

Therefore, the number of factors of 1260 that do not end with zero is 9 . Answer: Option D (12) is incorrect. Attention CAT Students! To make sure you are not studying endlessly, EduRev has designed CAT study material, with Structured Courses, Videos, & Test Series.

What is the trick to finding all factors of a number?

How to Find Factors of Large Numbers? To calculate the factors of large numbers, divide the numbers with the least prime number , i.e. 2. If the number is not divisible by 2, move to the next prime numbers, i.e. 3 and so on until 1 is reached. Below is an example to find the factors of a large number.

What is the formula for finding factors?

For a number N, whose prime factorization is X a × Y b , we get the total number of factors by adding 1 to each exponent and then multiplying these together. This expresses the number of factors formula as, (a + 1) × (b + 1) , where a, and b are the exponents obtained after the prime factorization of the given number.

What are the multiples of 1260?

What are the Multiples of 1260? So, the first 10 multiples of 1260 are: 1260, 2520, 3780, 5040, 5040, 7560, 8820, 10080, 11340 and 12600 .

How to find even factors of a number?

To find the number of even factors, we can multiply the number of odd factors by the power of 2 (not the power of 2 + 1!!!). For 540, we have (3 + 1)(1 + 1)(2) = 16 even factors. Of course, also note that the total number of factors = the number of even factors + the number of odd factors.

What is the smallest whole number by which 1260 must be multiplied to get a perfect square?

Answer. It will be 35 to be multiplied by the given number , to get a perfect square........

What is the easiest way to teach factors?

One of the easiest ways for children to calculate factors is to use a factor tree . This is a simple method used to work out which numbers can be multiplied together to reach a product.

What is the shortcut to find the number of factors of a number?

Do the prime factorization of the number. Add 1 to each exponent (including an exponent of 1), and multiply these exponents together . Let's say the number is 5040. 5040 = 2^4 x 3^2 x 5 x 7 So, add 1 to each exponent and multiply these exponents together: 5 x 3 x 2 x 2 = 60, So 5040 should have 60 positive factors.

What is the factor formula?

Factoring formulas are used to write an algebraic expression as the product of two or more expressions . Some important factoring formulas are given as, (a + b) 2 = a 2 + 2ab + b. (a - b) 2 = a 2 - 2ab + b.

How many factors does 72 have?

Factor list of 72. Therefore the factors of 72 are 1, 2, 3, 4, 6, 8, 9, 12, 18, 24, 36 and 72 .

Factors of 1260 - Learn how to find factors of a given number (2024)

2. Steps to find factors of 1260 using Prime Factorization

A prime number is a number that has exactly two factors, 1 and the number itself. Prime factorization of a number means breaking down of the number into the form of products of its prime factors.

There are two different methods that can be used for the prime factorization.

Method 1: Division Method

To find the primefactors of 1260 using the division method, follow these steps:

Step 1. Start dividing 1260 by the smallest prime number, i.e., 2, 3, 5, and so on. Find the smallest prime factor of the number.
Step 2. After finding the smallest prime factor of the number 1260, which is 2. Divide 1260 by 2 to obtain the quotient (630).
1260 ÷ 2 = 630
Step 3. Repeat step 1 with the obtained quotient (630).
630 ÷ 2 = 315

315 ÷ 3 = 105

105 ÷ 3 = 35

35 ÷ 5 = 7

7 ÷ 7 = 1

So, the prime factorization of 1260 is, 1260 = 2 x 2 x 3 x 3 x 5 x 7.

Method 2: Factor Tree Method

We can follow the same procedure using the factor tree of 1260 as shown below:

So, the prime factorization of 1260 is, 1260 = 2 x 2 x 3 x 3 x 5 x 7.

3. Find factors of 1260 in Pairs

Pair factors of a number are any two numbers which, which on multiplying together, give that number as a result. The pair factors of 1260 would be the two numbers which, when multiplied, give 1260 as the result.

The following table represents the calculation of factors of 1260 in pairs:

Factor Pair	Pair Factorization
1 and 1260	1 x 1260 = 1260
2 and 630	2 x 630 = 1260
3 and 420	3 x 420 = 1260
4 and 315	4 x 315 = 1260
5 and 252	5 x 252 = 1260
6 and 210	6 x 210 = 1260
7 and 180	7 x 180 = 1260
9 and 140	9 x 140 = 1260
10 and 126	10 x 126 = 1260
12 and 105	12 x 105 = 1260
14 and 90	14 x 90 = 1260
15 and 84	15 x 84 = 1260
18 and 70	18 x 70 = 1260
20 and 63	20 x 63 = 1260
21 and 60	21 x 60 = 1260
28 and 45	28 x 45 = 1260
30 and 42	30 x 42 = 1260
35 and 36	35 x 36 = 1260

Since the product of two negative numbers gives a positive number, the product of the negative values of both the numbers in a pair factor will also give 1260. They are called negative pair factors.

Hence, the negative pairs of 1260 would be ( -1 , -1260 ) , ( -2 , -630 ) , ( -3 , -420 ) , ( -4 , -315 ) , ( -5 , -252 ) , ( -6 , -210 ) , ( -7 , -180 ) , ( -9 , -140 ) , ( -10 , -126 ) , ( -12 , -105 ) , ( -14 , -90 ) , ( -15 , -84 ) , ( -18 , -70 ) , ( -20 , -63 ) , ( -21 , -60 ) , ( -28 , -45 ) , ( -30 , -42 ) and ( -35 , -36 ) .

What are factors?

In mathematics, a factor is that number which divides into another number exactly, without leaving a remainder. A factor of a number can be positive or negative.

Properties of factors

Each number is a factor of itself. Eg. 1260 is a factor of itself.
1 is a factor of every number. Eg. 1 is a factor of 1260.
Every number is a factor of zero (0), since 1260 x 0 = 0.
Every number other than 1 has at least two factors, namely the number itself and 1.
Every factor of a number is an exact divisor of that number, example 1, 2, 3, 4, 5, 6, 7, 9, 10, 12, 14, 15, 18, 20, 21, 28, 30, 35, 36, 42, 45, 60, 63, 70, 84, 90, 105, 126, 140, 180, 210, 252, 315, 420, 630, 1260 are exact divisors of 1260.
Factors of 1260 are 1, 2, 3, 4, 5, 6, 7, 9, 10, 12, 14, 15, 18, 20, 21, 28, 30, 35, 36, 42, 45, 60, 63, 70, 84, 90, 105, 126, 140, 180, 210, 252, 315, 420, 630, 1260. Each factor divides 1260 without leaving a remainder.
Every factor of a number is less than or equal to the number, eg. 1, 2, 3, 4, 5, 6, 7, 9, 10, 12, 14, 15, 18, 20, 21, 28, 30, 35, 36, 42, 45, 60, 63, 70, 84, 90, 105, 126, 140, 180, 210, 252, 315, 420, 630, 1260 are all less than or equal to 1260.

Frequently Asked Questions

Which is the smallest prime factor of 1260?
Smallest prime factor of 1260 is 2.
Is 1260 a perfect square?
No 1260 is not a perfect square.
What are five multiples of 1260?
First five multiples of 1260 are 2520, 3780, 5040, 6300, 7560.
What is prime factorization of 1260?
Prime factorization of 1260 is 2 x 2 x 3 x 3 x 5 x 7.
What are factors of 1260?
Factors of 1260 are 1, 2, 3, 4, 5, 6, 7, 9, 10, 12, 14, 15, 18, 20, 21, 28, 30, 35, 36, 42, 45, 60, 63, 70, 84, 90, 105, 126, 140, 180, 210, 252, 315, 420, 630, 1260.
How do you find factors of a negative number? ( eg. -1260 )?
Factors of -1260 are -1, -2, -3, -4, -5, -6, -7, -9, -10, -12, -14, -15, -18, -20, -21, -28, -30, -35, -36, -42, -45, -60, -63, -70, -84, -90, -105, -126, -140, -180, -210, -252, -315, -420, -630, -1260.
Is 1260 a whole number?
Yes 1260 is a whole number.
Which is greatest factor of 1260?
The greatest factor of 1260 is 630.
What are the prime factors of 1260?
The factors of 1260 are 1, 2, 3, 4, 5, 6, 7, 9, 10, 12, 14, 15, 18, 20, 21, 28, 30, 35, 36, 42, 45, 60, 63, 70, 84, 90, 105, 126, 140, 180, 210, 252, 315, 420, 630, 1260.Prime factors of 1260 are 2, 2, 3, 3, 5, 7.

Examples of Factors

Ariel has been assigned the task to find the product of all the prime factors of 1260. Can you help her?

Prime factors of 1260 are 2, 2, 3, 3, 5, 7.Hence, the product of prime factors of 210.

Can you help Rubel to find out the product of the even factors of 1260?

Factors of 1260 are 1, 2, 3, 4, 5, 6, 7, 9, 10, 12, 14, 15, 18, 20, 21, 28, 30, 35, 36, 42, 45, 60, 63, 70, 84, 90, 105, 126, 140, 180, 210, 252, 315, 420, 630, 1260.Even factors of 1260 are 2, 4, 6, 10, 12, 14, 18, 20, 28, 30, 36, 42, 60, 70, 84, 90, 126, 140, 180, 210, 252, 420, 630, 1260.Hence, product of even factors of 1260 is; 2 x 4 x 6 x 10 x 12 x 14 x 18 x 20 x 28 x 30 x 36 x 42 x 60 x 70 x 84 x 90 x 126 x 140 x 180 x 210 x 252 x 420 x 630 x 1260 = 6.558529697156825e+40.

Joy wants to calculate mean of all the factors of 1260. Help him in finding the mean of 1260.

Factors of 1260 are 1, 2, 3, 4, 5, 6, 7, 9, 10, 12, 14, 15, 18, 20, 21, 28, 30, 35, 36, 42, 45, 60, 63, 70, 84, 90, 105, 126, 140, 180, 210, 252, 315, 420, 630, 1260.To calculate the mean we need to calculate the sum of factors first. Sum of factors of 1260 is 1 + 2 + 3 + 4 + 5 + 6 + 7 + 9 + 10 + 12 + 14 + 15 + 18 + 20 + 21 + 28 + 30 + 35 + 36 + 42 + 45 + 60 + 63 + 70 + 84 + 90 + 105 + 126 + 140 + 180 + 210 + 252 + 315 + 420 + 630 + 1260 = 4368.Hence, the mean of factors of 1260 is 4368 ÷ 36 = 121.33.

Annie's mathematics teacher has asked her to find out all the positive and negative factors of 1260? Help her in writing all the factors.

Positive factors are 1, 2, 3, 4, 5, 6, 7, 9, 10, 12, 14, 15, 18, 20, 21, 28, 30, 35, 36, 42, 45, 60, 63, 70, 84, 90, 105, 126, 140, 180, 210, 252, 315, 420, 630, 1260. Negative factors are -1, -2, -3, -4, -5, -6, -7, -9, -10, -12, -14, -15, -18, -20, -21, -28, -30, -35, -36, -42, -45, -60, -63, -70, -84, -90, -105, -126, -140, -180, -210, -252, -315, -420, -630, -1260.

How many factors are there for 1260?

Factors of 1260 are 1, 2, 3, 4, 5, 6, 7, 9, 10, 12, 14, 15, 18, 20, 21, 28, 30, 35, 36, 42, 45, 60, 63, 70, 84, 90, 105, 126, 140, 180, 210, 252, 315, 420, 630, 1260.So there are in total 36 factors.

Joey wants to write all the prime factors of 1260 in exponential form, but he doesn't know how to do so can you assist him in this task?

Prime factors of 1260 are 2, 2, 3, 3, 5, 7.So in exponential form it can be written as 2² x 3² x 5 x 7.

Kevin has been asked to write 35 factor(s) of 1260. Can you predict the answer?

35 factor(s) of 1260 are 1, 2, 3, 4, 5, 6, 7, 9, 10, 12, 14, 15, 18, 20, 21, 28, 30, 35, 36, 42, 45, 60, 63, 70, 84, 90, 105, 126, 140, 180, 210, 252, 315, 420, 630.