1. Steps to find factors of 1470 using Division Method

Example: Find factors of 1470

  • Divide 1470 by 1: 1470 ÷ 1 : Remainder = 0
  • Divide 1470 by 2: 1470 ÷ 2 : Remainder = 0
  • Divide 1470 by 3: 1470 ÷ 3 : Remainder = 0
  • Divide 1470 by 5: 1470 ÷ 5 : Remainder = 0
  • Divide 1470 by 6: 1470 ÷ 6 : Remainder = 0
  • Divide 1470 by 7: 1470 ÷ 7 : Remainder = 0
  • Divide 1470 by 10: 1470 ÷ 10 : Remainder = 0
  • Divide 1470 by 14: 1470 ÷ 14 : Remainder = 0
  • Divide 1470 by 15: 1470 ÷ 15 : Remainder = 0
  • Divide 1470 by 21: 1470 ÷ 21 : Remainder = 0
  • Divide 1470 by 30: 1470 ÷ 30 : Remainder = 0
  • Divide 1470 by 35: 1470 ÷ 35 : Remainder = 0
  • Divide 1470 by 42: 1470 ÷ 42 : Remainder = 0
  • Divide 1470 by 49: 1470 ÷ 49 : Remainder = 0
  • Divide 1470 by 70: 1470 ÷ 70 : Remainder = 0
  • Divide 1470 by 98: 1470 ÷ 98 : Remainder = 0
  • Divide 1470 by 105: 1470 ÷ 105 : Remainder = 0
  • Divide 1470 by 147: 1470 ÷ 147 : Remainder = 0
  • Divide 1470 by 210: 1470 ÷ 210 : Remainder = 0
  • Divide 1470 by 245: 1470 ÷ 245 : Remainder = 0
  • Divide 1470 by 294: 1470 ÷ 294 : Remainder = 0
  • Divide 1470 by 490: 1470 ÷ 490 : Remainder = 0
  • Divide 1470 by 735: 1470 ÷ 735 : Remainder = 0
  • Divide 1470 by 1470: 1470 ÷ 1470 : Remainder = 0

Hence, Factors of 1470 are 1, 2, 3, 5, 6, 7, 10, 14, 15, 21, 30, 35, 42, 49, 70, 98, 105, 147, 210, 245, 294, 490, 735, and 1470

2. Steps to find factors of 1470 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 1470 using the division method, follow these steps:

  • Step 1. Start dividing 1470 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 1470, which is 2. Divide 1470 by 2 to obtain the quotient (735).
    1470 ÷ 2 = 735
  • Step 3. Repeat step 1 with the obtained quotient (735).
    735 ÷ 3 = 245
    245 ÷ 5 = 49
    49 ÷ 7 = 7
    7 ÷ 7 = 1

So, the prime factorization of 1470 is, 1470 = 2 x 3 x 5 x 7 x 7.

Method 2: Factor Tree Method

We can follow the same procedure using the factor tree of 1470 as shown below:

So, the prime factorization of 1470 is, 1470 = 2 x 3 x 5 x 7 x 7.

3. Find factors of 1470 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 1470 would be the two numbers which, when multiplied, give 1470 as the result.

The following table represents the calculation of factors of 1470 in pairs:

Factor Pair Pair Factorization
1 and 1470 1 x 1470 = 1470
2 and 735 2 x 735 = 1470
3 and 490 3 x 490 = 1470
5 and 294 5 x 294 = 1470
6 and 245 6 x 245 = 1470
7 and 210 7 x 210 = 1470
10 and 147 10 x 147 = 1470
14 and 105 14 x 105 = 1470
15 and 98 15 x 98 = 1470
21 and 70 21 x 70 = 1470
30 and 49 30 x 49 = 1470
35 and 42 35 x 42 = 1470

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 1470. They are called negative pair factors.

Hence, the negative pairs of 1470 would be ( -1 , -1470 ) , ( -2 , -735 ) , ( -3 , -490 ) , ( -5 , -294 ) , ( -6 , -245 ) , ( -7 , -210 ) , ( -10 , -147 ) , ( -14 , -105 ) , ( -15 , -98 ) , ( -21 , -70 ) , ( -30 , -49 ) and ( -35 , -42 ) .

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. 1470 is a factor of itself.
  • 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, 5, 6, 7, 10, 14, 15, 21, 30, 35, 42, 49, 70, 98, 105, 147, 210, 245, 294, 490, 735, 1470 are exact divisors of 1470.
  • 1 is a factor of every number. Eg. 1 is a factor of 1470.
  • Every number is a factor of zero (0), since 1470 x 0 = 0.

Frequently Asked Questions

  • What are the prime factors of 1470?

    The factors of 1470 are 1, 2, 3, 5, 6, 7, 10, 14, 15, 21, 30, 35, 42, 49, 70, 98, 105, 147, 210, 245, 294, 490, 735, 1470.
    Prime factors of 1470 are 2, 3, 5, 7, 7.

  • What two numbers make 1470?

    Two numbers that make 1470 are 2 and 735.

  • What is the greatest prime factors of 1470?

    The greatest prime factor of 1470 is 7.

  • What are factors of 1470?

    Factors of 1470 are 1, 2, 3, 5, 6, 7, 10, 14, 15, 21, 30, 35, 42, 49, 70, 98, 105, 147, 210, 245, 294, 490, 735, 1470.

  • How do you find factors of a negative number? ( eg. -1470 )?

    Factors of -1470 are -1, -2, -3, -5, -6, -7, -10, -14, -15, -21, -30, -35, -42, -49, -70, -98, -105, -147, -210, -245, -294, -490, -735, -1470.

  • What are five multiples of 1470?

    First five multiples of 1470 are 2940, 4410, 5880, 7350, 8820.

  • Write some multiples of 1470?

    First five multiples of 1470 are 2940, 4410, 5880, 7350.

  • Is 1470 a perfect square?

    No 1470 is not a perfect square.

  • What two numbers make 1470?

    Two numbers that make 1470 are 2 and 735.

Examples of Factors

What is prime factorization of 1470?

Prime factorization of 1470 is 2 x 3 x 5 x 7 x 7 = 2 x 3 x 5 x 72.

Sammy is puzzled while calculating the prime factors of 1470. Can you help him find them?

Factors of 1470 are 1, 2, 3, 5, 6, 7, 10, 14, 15, 21, 30, 35, 42, 49, 70, 98, 105, 147, 210, 245, 294, 490, 735, 1470.
Prime factors of 1470 are 2, 3, 5, 7, 7

Kevin has been asked to write 23 factor(s) of 1470. Can you predict the answer?

23 factor(s) of 1470 are 1, 2, 3, 5, 6, 7, 10, 14, 15, 21, 30, 35, 42, 49, 70, 98, 105, 147, 210, 245, 294, 490, 735.

Joey wants to write all the prime factors of 1470 in exponential form, but he doesn't know how to do so can you assist him in this task?

Prime factors of 1470 are 2, 3, 5, 7, 7.
So in exponential form it can be written as 2 x 3 x 5 x 72.

How many factors are there for 1470?

Factors of 1470 are 1, 2, 3, 5, 6, 7, 10, 14, 15, 21, 30, 35, 42, 49, 70, 98, 105, 147, 210, 245, 294, 490, 735, 1470.
So there are in total 24 factors.

Annie's mathematics teacher has asked her to find out all the positive and negative factors of 1470? Help her in writing all the factors.

Positive factors are 1, 2, 3, 5, 6, 7, 10, 14, 15, 21, 30, 35, 42, 49, 70, 98, 105, 147, 210, 245, 294, 490, 735, 1470.
Negative factors are -1, -2, -3, -5, -6, -7, -10, -14, -15, -21, -30, -35, -42, -49, -70, -98, -105, -147, -210, -245, -294, -490, -735, -1470.

Can you help Rubel to find out the product of the even factors of 1470?

Factors of 1470 are 1, 2, 3, 5, 6, 7, 10, 14, 15, 21, 30, 35, 42, 49, 70, 98, 105, 147, 210, 245, 294, 490, 735, 1470.
Even factors of 1470 are 2, 6, 10, 14, 30, 42, 70, 98, 210, 294, 490, 1470.
Hence, product of even factors of 1470 is; 2 x 6 x 10 x 14 x 30 x 42 x 70 x 98 x 210 x 294 x 490 x 1470 = 645779095649856000000.