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Factors of 1470

Factors of 1470 are integers that can be divided evenly into 1470. There are overall 24 factors of 1470 among which 1470 is the biggest factor and its prime factors are 2, 3, 5, 7. The sum of all factors of 1470 is 4104.

  • All Factors of 1470: 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
  • Prime Factors of 1470: 2, 3, 5, 7
  • Prime Factorization of 1470: 21 × 31 × 51 × 72
  • Sum of Factors of 1470: 4104
1. What Are the Factors of 1470?
2. Factors of 1470 by Prime Factorization
3. Factors of 1470 in Pairs
4. FAQs on Factors of 1470
Factors of 1470

What are Factors of 1470?

Factors of 1470 are pairs of those numbers whose products result in 1470. These factors are either prime numbers or composite numbers.

How to Find the Factors of 1470?

To find the factors of 1470, we will have to find the list of numbers that would divide 1470 without leaving any remainder.

  • 1470/147 = 10; therefore, 147 is a factor of 1470 and 10 is also a factor of 1470.
  • 1470/2 = 735; therefore, 2 is a factor of 1470 and 735 is also a factor of 1470.
Similarly we can find other factors. Hence, 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.

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Factors of 1470 by Prime Factorization

The number 1470 is composite and therefore it will have prime factors. Now let us learn how to calculate the prime factors of 1470. The first step is to divide the number 1470 with the smallest prime factor, here it is 2. We keep dividing until it gives a non-zero remainder.
  • 1470 ÷ 2 = 735

Further dividing 735 by 2 gives a non-zero remainder. So we stop the process and continue dividing the number 735 by the next smallest prime factor. We stop ultimately if the next prime factor doesn't exist or when we can't divide any further.

So, the prime factorization of 1470 can be written as 21 × 31 × 51 × 72 where 2, 3, 5, 7 are prime.

 

Factors of 1470 in Pairs

Pair factors of 1470 are the pairs of numbers that when multiplied give the product 1470. The factors of 1470 in pairs are:

  • 1 × 1470 = (1, 1470)
  • 2 × 735 = (2, 735)
  • 3 × 490 = (3, 490)
  • 5 × 294 = (5, 294)
  • 6 × 245 = (6, 245)
  • 7 × 210 = (7, 210)
  • 10 × 147 = (10, 147)
  • 14 × 105 = (14, 105)
  • 15 × 98 = (15, 98)
  • 21 × 70 = (21, 70)
  • 30 × 49 = (30, 49)
  • 35 × 42 = (35, 42)

Negative pair factors of 1470 are:

  • -1 × -1470 = (-1, -1470)
  • -2 × -735 = (-2, -735)
  • -3 × -490 = (-3, -490)
  • -5 × -294 = (-5, -294)
  • -6 × -245 = (-6, -245)
  • -7 × -210 = (-7, -210)
  • -10 × -147 = (-10, -147)
  • -14 × -105 = (-14, -105)
  • -15 × -98 = (-15, -98)
  • -21 × -70 = (-21, -70)
  • -30 × -49 = (-30, -49)
  • -35 × -42 = (-35, -42)

NOTE: If (a, b) is a pair factor of a number then (b, a) is also a pair factor of that number.

Factors of 1470 Solved Examples

  1. Example 1: How many factors are there for 1470?

    Solution:

    The factors of 1470 are too many, therefore if we can find the prime factorization of 1470, then the total number of factors can be calculated using the formula shown below.
    If the prime factorization of the number is ax × by × cz where a, b, c are prime, then the total number of factors can be given by (x + 1)(y + 1)(z + 1).

    Prime Factorization of 1470 = 21 × 31 × 51 × 72
    Therefore, the total number of factors are (1 + 1) × (1 + 1) × (1 + 1) × (2 + 1) = 2 × 2 × 2 × 3 = 24

  2. Example 2: Find the Lowest Common Multiple (LCM) and Highest Common Factor (HCF) of 1470 and 1076.

    Solution:

    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 and factors of 1076 are 1, 2, 4, 269, 538, 1076.

    Therefore, the Lowest Common Multiple (LCM) of 1470 and 1076 is 790860 and Highest Common Factor (HCF) of 1470 and 1076 is 2.

  3. Example 3: Find if 6, 14, 70, 147, 245, 490, 544 and 1470 are factors of 1470.

    Solution:

    When we divide 1470 by 544 it leaves a remainder. Therefore, the number 544 is not a factor of 1470. All numbers except 544 are factors of 1470.

  4. Example 4: Find the product of all the prime factors of 1470.

    Solution:

    Since, the prime factors of 1470 are 2, 3, 5, 7. Therefore, the product of prime factors = 2 × 3 × 5 × 7 = 210.

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FAQs on Factors of 1470

What are the 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 and its 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.

What is the Sum of all Factors of 1470?

Sum of all factors of 1470 = (21 + 1 - 1)/(2 - 1) × (31 + 1 - 1)/(3 - 1) × (51 + 1 - 1)/(5 - 1) × (72 + 1 - 1)/(7 - 1) = 4104

What are the Pair Factors of 1470?

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

What is the Greatest Common Factor of 1470 and 1114?

The factors of 1470 and 1114 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 and 1, 2, 557, 1114 respectively.

Common factors of 1470 and 1114 are [1, 2].

Hence, the Greatest Common Factor of 1470 and 1114 is 2.

How Many Factors of 1470 are also common to the Factors of 604?

Since, 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 and the factors of 604 are 1, 2, 4, 151, 302, 604.
Hence, [1, 2] are the common factors of 1470 and 604.

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