Factors of 70: Definition, List & How to Find Them

The concept of factors of 70 is a fundamental building block in mathematics, helping students solve division, multiplication, LCM, and HCF problems, as well as many real-life scenarios and exam questions.

What Are Factors of 70?

A factor of 70 is any whole number that divides 70 exactly, leaving no remainder. In other words, if we multiply two whole numbers and get 70 as the answer, both numbers are factors of 70. This idea is used to solve questions in topics like divisibility, multiples, and factorization. Some examples include (2 × 35 = 70) and (5 × 14 = 70), so 2, 5, 14, and 35 are all factors of 70.

Key Formula for Factors of 70

There isn’t a single formula for factors, but a helpful step is:
To find all factors of 70, check which numbers between 1 and 70 divide 70 evenly.
Or, use prime factorization:
\( 70 = 2 \times 5 \times 7 \)

Step-by-Step Factorization of 70

1. Start with the number 70.
2. Check numbers from 1 up to 70. If 70 divided by a number gives no remainder, it’s a factor of 70.
3. List the factor pairs:
   
   1 × 70 = 70
   2 × 35 = 70
   5 × 14 = 70
   7 × 10 = 70
   
4. Write all positive factors in order: 1, 2, 5, 7, 10, 14, 35, 70.

Prime Factorization of 70

The prime factors of 70 are the prime numbers that multiply together to make 70. Here’s how:

1. 70 divided by 2 (smallest prime number): 70 ÷ 2 = 35
2. 35 divided by 5 (next lowest prime): 35 ÷ 5 = 7
3. 7 is a prime number and can’t be divided further.
4. So, prime factorization of 70 = 2 × 5 × 7

Factor Pairs of 70

Factor Pair	Product
(1, 70)	1 × 70 = 70
(2, 35)	2 × 35 = 70
(5, 14)	5 × 14 = 70
(7, 10)	7 × 10 = 70

Even and Odd Factors of 70

The even factors of 70 are 2, 10, 14, 70. The odd factors of 70 are 1, 5, 7, 35.

Negative Factors of 70

Every positive factor of 70 also has a negative pair. So, negative factors are -1, -2, -5, -7, -10, -14, -35, and -70.

Speed Trick or Vedic Shortcut

Here’s a quick way to find factor pairs: For any number, list numbers up to its square root and check if division leaves no remainder. For 70, √70 ≈ 8.3, so check 1 through 8:

The quotients (70, 35, 14, 10) and divisors (1, 2, 5, 7) make all the pairs!

This saves time in math olympiads and competitive exams. Vedantu teachers share more such exam tricks in live sessions!

Students’ Common Mistakes

• Mixing factors with multiples of 70 (multiples are 70, 140, 210...)
• Forgetting to include 1 and 70 as factors.
• Missing factor pairs (e.g., omitting 2 and 35)

Relation to Other Concepts

Understanding the factors of 70 helps with prime factorization, LCM, HCF, and divisibility rules. Mastering this makes it easier to handle harder questions in algebra and problem solving.

Try These Yourself

• List all factors of 70.
• Is 14 a factor of 70?
• Write all even factors of 70.
• Find the sum of all factors of 70.

Practice Questions on Factors of 70

1. What is the greatest factor of 70 apart from 70 itself?
2. Which of these are factors of 70: 6, 14, 21, 35?
3. Find the common factors of 70 and 35.
4. What is the LCM of 70 and 60?

Answers:
1. 35
2. 14, 35
3. 1, 5, 7, 35
4. 420 (LCM of 70 and 60)

Frequently Made Errors and Misunderstandings

• Thinking decimals or fractions (e.g., 3.5) can be factors (only whole numbers can be factors).
• Missing negative factors in some types of exam questions.

Related Concepts and Internal Links

For more on factorization tricks and related numbers, see these:

• Factors of 60
• Factors of 35
• LCM and HCF

Classroom Tip

A quick way to remember: If you can draw a multiplication table with 70 as the answer, both numbers used are factors. For competitive exams, make a factor table and practice with similar numbers (like 60 or 80) for speed. Vedantu’s live doubt sessions also help consolidate this concept!

We explored the factors of 70 — from definition, stepwise listing, speed tips, mistakes to avoid, and connections to other topics. With regular practice at Vedantu, you’ll gain mastery in factorization and solving related problems easily!