What is the prime factorization of 140?

The number 140 is an even composite number. This means it has factors other than 1 and itself. In mathematics, the process of breaking down a composite number into the product of its prime factors is known as prime factorization. Let's explore the prime factorization of 140 in detail along with its factors and factor pairs.

Factors of 140

The factors of 140 are the numbers that divide 140 completely without leaving any remainder. These factors include:

• 1
• 2
• 4
• 5
• 7
• 10
• 14
• 20
• 28
• 35
• 70
• 140

Prime Factorization of 140

Prime factorization involves expressing a number as the product of its prime factors. For the number 140, we can perform prime factorization as follows:

1. Divide 140 by the smallest prime number, 2: 140 ÷ 2 = 70.
2. Divide 70 by 2 again: 70 ÷ 2 = 35.
3. Next, divide 35 by 5: 35 ÷ 5 = 7.
4. Finally, divide 7 by 7: 7 ÷ 7 = 1.

Thus, the prime factorization of 140 is:

140 = 2 × 2 × 5 × 7

Factors of 140 in Pairs

Factor pairs are two numbers that, when multiplied, give 140. The factor pairs of 140 are:

• (1, 140)
• (2, 70)
• (4, 35)
• (5, 28)
• (7, 20)
• (10, 14)

Important Notes

• The factors of 140 are all the numbers that divide 140 exactly without any remainder.
• The prime factorization of 140 is expressed as a product of its prime numbers: 2 × 2 × 5 × 7.
• Each factor pair consists of two numbers that multiply to give 140.

Methods to Calculate Factors

You can calculate the factors of 140 using either the division method or prime factorization. The division method involves dividing 140 by whole numbers to identify divisors, while prime factorization of 140 involves breaking it down into prime numbers. Both methods yield the same result.