Factors of 1764 are the list of integers that we can split evenly into 1764. There are overall 27 factors of 1764 among which 1764 is the biggest factor and its prime factors are 2, 3, 7. The Prime Factorization of 1764 is 22 × 32 × 72.

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All Factors of 1764: 1, 2, 3, 4, 6, 7, 9, 12, 14, 18, 21, 28, 36, 42, 49, 63, 84, 98, 126, 147, 196, 252, 294, 441, 588, 882 and 1764 Prime Factors of 1764: 2, 3, 7 Prime Factorization of 1764: 22 × 32 × 72 Sum of Factors of 1764: 5187
1.What Are the Factors of 1764?
2.Factors of 1764 by Prime Factorization
3.Factors of 1764 in Pairs
4.FAQs on Factors of 1764
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What are Factors of 1764?


Factors of 1764 are pairs of those numbers whose products result in 1764. These factors are either prime numbers or composite numbers.

How to Find the Factors of 1764?

To find the factors of 1764, we will have to find the list of numbers that would divide 1764 without leaving any remainder.

1764/6 = 294; therefore, 6 is a factor of 1764 and 294 is also a factor of 1764.1764/4 = 441; therefore, 4 is a factor of 1764 and 441 is also a factor of 1764. Similarly we can find other factors. Hence, the factors of 1764 are 1, 2, 3, 4, 6, 7, 9, 12, 14, 18, 21, 28, 36, 42, 49, 63, 84, 98, 126, 147, 196, 252, 294, 441, 588, 882, 1764.

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Factors of 1764 by Prime Factorization


The number 1764 is composite and therefore it will have prime factors. Now let us learn how to calculate the prime factors of 1764. The first step is to divide the number 1764 with the smallest prime factor, here it is 2. We keep dividing until it gives a non-zero remainder. 1764 ÷ 2 = 882 882 ÷ 2 = 441

Further dividing 441 by 2 gives a non-zero remainder. So we stop the process and continue dividing the number 441 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 1764 can be written as 22 × 32 × 72 where 2, 3, 7 are prime.


Factors of 1764 in Pairs


Pair factors of 1764 are the pairs of numbers that when multiplied give the product 1764. The factors of 1764 in pairs are:

1 × 1764 = (1, 1764) 2 × 882 = (2, 882) 3 × 588 = (3, 588) 4 × 441 = (4, 441) 6 × 294 = (6, 294) 7 × 252 = (7, 252) 9 × 196 = (9, 196) 12 × 147 = (12, 147) 14 × 126 = (14, 126) 18 × 98 = (18, 98) 21 × 84 = (21, 84) 28 × 63 = (28, 63) 36 × 49 = (36, 49) 42 × 42 = (42, 42)

Negative pair factors of 1764 are:

-1 × -1764 = (-1, -1764) -2 × -882 = (-2, -882) -3 × -588 = (-3, -588) -4 × -441 = (-4, -441) -6 × -294 = (-6, -294) -7 × -252 = (-7, -252) -9 × -196 = (-9, -196) -12 × -147 = (-12, -147) -14 × -126 = (-14, -126) -18 × -98 = (-18, -98) -21 × -84 = (-21, -84) -28 × -63 = (-28, -63) -36 × -49 = (-36, -49) -42 × -42 = (-42, -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 1764 Solved Examples


Example 1: How many factors are there for 1764?

Solution:

The factors of 1764 are too many, therefore if we can find the prime factorization of 1764, 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 1764 = 22 × 32 × 72 Therefore, the total number of factors are (2 + 1) × (2 + 1) × (2 + 1) = 3 × 3 × 3 = 27


Example 3: Find if 3, 7, 14, 18, 42, 63, 588 and 817 are factors of 1764.

Solution:

When we divide 1764 by 817 it leaves a remainder. Therefore, the number 817 is not a factor of 1764. All numbers except 817 are factors of 1764.


Example 4: Find the product of all the prime factors of 1764.

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Solution:

Since, the prime factors of 1764 are 2, 3, 7. Therefore, the product of prime factors = 2 × 3 × 7 = 42.


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FAQs on Factors of 1764


What are the Factors of 1764?

The factors of 1764 are 1, 2, 3, 4, 6, 7, 9, 12, 14, 18, 21, 28, 36, 42, 49, 63, 84, 98, 126, 147, 196, 252, 294, 441, 588, 882, 1764 and its negative factors are -1, -2, -3, -4, -6, -7, -9, -12, -14, -18, -21, -28, -36, -42, -49, -63, -84, -98, -126, -147, -196, -252, -294, -441, -588, -882, -1764.

What is the Sum of all the Factors of 1764?

Sum of all factors of 1764 = (22 + 1 - 1)/(2 - 1) × (32 + 1 - 1)/(3 - 1) × (72 + 1 - 1)/(7 - 1) = 5187

What numbers are the Pair Factors of 1764?

The pair factors of 1764 are (1, 1764), (2, 882), (3, 588), (4, 441), (6, 294), (7, 252), (9, 196), (12, 147), (14, 126), (18, 98), (21, 84), (28, 63), (36, 49), (42, 42).

What is the Greatest Common Factor of 1764 and 152?

The factors of 1764 and 152 are 1, 2, 3, 4, 6, 7, 9, 12, 14, 18, 21, 28, 36, 42, 49, 63, 84, 98, 126, 147, 196, 252, 294, 441, 588, 882, 1764 and 1, 2, 4, 8, 19, 38, 76, 152 respectively. Common factors of 1764 and 152 are <1, 2, 4>. Hence, the GCF of 1764 and 152 is 4.

How Many Factors of 1231 are also common to the Factors of 1764?

Since, the factors of 1764 are 1, 2, 3, 4, 6, 7, 9, 12, 14, 18, 21, 28, 36, 42, 49, 63, 84, 98, 126, 147, 196, 252, 294, 441, 588, 882, 1764 and factors of 1231 are 1, 1231. Hence, 1764 and 1231 have only one common factor which is 1. Therefore, 1764 and 1231 are co-prime.