Factors Of 77 - Pair Factors, Prime Factorization, Example And FAQs

The concept of factors of 77 is a key building block in mathematics, helping students understand divisibility, prime factorization, HCF/LCM, and number properties. Quickly recalling factor lists and their pairs is essential for exam revision and real-life applications like grouping or dividing objects evenly.

What Are Factors of 77?

A factor of 77 is any integer that divides 77 exactly, with no remainder. In other words, if you can multiply two whole numbers to get 77, both numbers are factors of 77. Factors are not the same as multiples; factors are always less than or equal to the number itself. Common related ideas include divisors of 77, factor pairings, and prime factorization.

List of Factors of 77

The complete list of factors of 77 is:

• 1
• 7
• 11
• 77

Each of these numbers divides 77 evenly, leaving no remainder. Negative factors also exist (e.g., -1, -7, -11, -77), but in most maths problems and exams, only positive factors are required.

Prime Factorization of 77

To find the prime factors of 77, break it down into numbers that are only divisible by 1 and themselves:

1. 77 is not divisible by 2, 3, 4, 5, or 6. 2. 77 ÷ 7 = 11 (both 7 and 11 are prime numbers). 3. So, 77 = 7 × 11.

So, the prime factorization of 77 is 7 × 11.

Step	Result
Divide by 7 (prime)	77 ÷ 7 = 11
Divide by 11 (prime)	11 ÷ 11 = 1

Factor Pairs of 77

Factor pairs are pairs of numbers that multiply to 77:

Pair	Product
(1, 77)	1 × 77 = 77
(7, 11)	7 × 11 = 77

Negative pairs such as (-1, -77) and (-7, -11) are also valid, since multiplying two negatives gives a positive.

Properties and Number Type

• 77 has more than two factors (1, 7, 11, 77), so it is a composite number (not prime).
• It is an odd number and not divisible by 2.
• The sum of all positive factors: 1 + 7 + 11 + 77 = 96.
• The highest common factor (HCF) of 77 and 56 is 7. Learn more: HCF of Two Numbers
• Understanding the difference between factors and multiples often helps speed up MCQ solving.

How to Find Factors of 77: Step-by-Step

1. Start with 1: 77 ÷ 1 = 77 (whole number, so 1 and 77 are factors) 2. Test 2 to 6: Not a whole number, so not factors 3. Divide by 7: 77 ÷ 7 = 11 (both 7 and 11 are factors) 4. Test 8 and onwards up to √77 (<9): No more whole-number results 5. List all found: 1, 7, 11, 77

Checking up to the square root ensures results are not repeated.

Speed Trick: Fast Checking for Factors

Exam tip: When asked "Is 77 a prime number?" just list up to √77 (about 8.7). Finding another divisor (like 7 or 11) means it's composite. Use divisibility rules for 7 and 11 for fast checking.

Practice Problems: Factors of 77

Try solving these problems with clear steps:

1. Find all the factors of 77. 1. List divisors of 77 up to 9 2. 77 ÷ 1 = 77 3. 77 ÷ 7 = 11 4. 77 ÷ 11 = 7 5. 77 ÷ 77 = 1 6. Answer: 1, 7, 11, 77
2. What is the prime factorization of 77? 1. Find smallest prime: 7 2. 77 ÷ 7 = 11 3. 11 is prime. So, 77 = 7 × 11
3. List all factor pairs of 77. 1. 1 × 77 = 77 2. 7 × 11 = 77 3. Answer: (1,77), (7,11)

Common Errors & Revision Tips

• Confusing factors and multiples (e.g., listing numbers larger than 77)
• Missing a factor by not checking up to the square root
• Forgetting factor pairs (especially (-1, -77) and (-7, -11) in advanced situations)
• Mixing up divisibility notions; remember, 77 is odd—not divisible by 2

Vedantu teachers recommend building a table or tree diagram for quick revision.

Relation to Other Maths Concepts

Knowing the factors of 77 helps with learning about prime factors, distinguishing composite numbers from primes, and solving for HCF and LCM in word problems.

Quick Check & Summary Table

Property	Value
Number of Positive Factors	4
Factors of 77	1, 7, 11, 77
Prime Factors	7, 11
Smallest Factor	1
Largest Factor	77

Wrapping It All Up

We explored factors of 77 from their definition, listing, prime factor breakdown, and factor pairs, all the way to common exam tricks for quick mental recall. Keep using Vedantu’s live classes and study resources for more number property insights and to master speed calculations for exams!

Suggested Lessons & Related Concepts

• Prime Factors
• Factors of a Number
• Composite Numbers
• Prime Factorization