Factors of 735 are integers that can be divided evenly into 735. There are 12 factors of 735 of which 735 itself is the biggest factor and its prime factors are 3, 5, 7 The sum of all factors of 735 is 1368.

• All Factors of 735: 1, 3, 5, 7, 15, 21, 35, 49, 105, 147, 245 and 735
• Prime Factors of 735: 3, 5, 7
• Prime Factorization of 735: 3¹ × 5¹ × 7²
• Sum of Factors of 735: 1368

1.	What Are the Factors of 735?
2.	Factors of 735 by Prime Factorization
3.	Factors of 735 in Pairs
4.	FAQs on Factors of 735

Factors of 735 are pairs of those numbers whose products result in 735. These factors are either prime numbers or composite numbers.

How to Find the Factors of 735?

To find the factors of 735, we will have to find the list of numbers that would divide 735 without leaving any remainder.

• 735/7 = 105; therefore, 7 is a factor of 735 and 105 is also a factor of 735.
• 735/147 = 5; therefore, 147 is a factor of 735 and 5 is also a factor of 735.

Similarly we can find other factors. Hence, the factors of 735 are 1, 3, 5, 7, 15, 21, 35, 49, 105, 147, 245, 735.

☛ Also Check:

• Factors of 108 - The factors of 108 are 1, 2, 3, 4, 6, 9, 12, 18, 27, 36, 54, 108
• Factors of 50 - The factors of 50 are 1, 2, 5, 10, 25, 50
• Factors of 10 - The factors of 10 are 1, 2, 5, 10
• Factors of 98 - The factors of 98 are 1, 2, 7, 14, 49, 98
• Factors of 34 - The factors of 34 are 1, 2, 17, 34

The number 735 is composite and therefore it will have prime factors. Now let us learn how to calculate the prime factors of 735. The first step is to divide the number 735 with the smallest prime factor, here it is 3. We keep dividing until it gives a non-zero remainder.

• 735 ÷ 3 = 245

Further dividing 245 by 3 gives a non-zero remainder. So we stop the process and continue dividing the number 245 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 735 can be written as 3¹ × 5¹ × 7² where 3, 5, 7 are prime.

Pair factors of 735 are the pairs of numbers that when multiplied give the product 735. The factors of 735 in pairs are:

• 1 × 735 = (1, 735)
• 3 × 245 = (3, 245)
• 5 × 147 = (5, 147)
• 7 × 105 = (7, 105)
• 15 × 49 = (15, 49)
• 21 × 35 = (21, 35)

Negative pair factors of 735 are:

• -1 × -735 = (-1, -735)
• -3 × -245 = (-3, -245)
• -5 × -147 = (-5, -147)
• -7 × -105 = (-7, -105)
• -15 × -49 = (-15, -49)
• -21 × -35 = (-21, -35)

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