164 LearnersLast updated on May 26th, 2025
Factors of 4860
Factors of 4860 are numbers that can divide 4860 completely without leaving a remainder. We often use factors in organizing events and seating arrangements in our daily lives. In this topic, we will learn more about the factors of 4860 and the different methods to find them
What are the Factors of 4860?
The factors of 4860 are all numbers that can divide 4860 evenly. These include positive and negative counterparts.
Positive Factors: 1, 2, 3, 4, 5, 6, 9, 10, 12, 15, 18, 20, 30, 36, 45, 54, 60, 90, 108, 120, 180, 243, 270, 360, 486, 540, 729, 972, 1215, 1458, 2430, and 4860.
Negative Factors: -1, -2, -3, -4, -5, -6, -9, -10, -12, -15, -18, -20, -30, -36, -45, -54, -60, -90, -108, -120, -180, -243, -270, -360, -486, -540, -729, -972, -1215, -1458, -2430, and -4860.
Prime Factors of 4860
Prime factors are the prime numbers themselves that, when multiplied together, give 4860 as the product.
Prime factors of 4860: 2, 3, 5, 7
Prime Factorization of 4860
Prime factorization involves breaking 4860 down into its prime factors.
Prime Factorization: 4860 = 22× 35× 51 × 71
How to Find the Factors of 4860?
There are various methods to find the factors of 4860
Methods to find the factors of 4860:
Multiplication Method
Division Method
Prime Factor and Prime Factorization
Factor Tree
Finding Factors Using Multiplication
The multiplication method involves finding pairs of numbers whose product is 4860.
Step 1: Find the pair of numbers whose product is 4860.
Step 2: The factors are those numbers, which when multiplied, yield 4860.
Step 3: List these numbers to identify all the factors.
1 × 4860 = 4860
2 × 2430 = 4860
3 × 1620 = 4860
Finding Factors by Division Method
The division method involves finding numbers that fully divide 4860.
Step 1: Start with 1, which is a factor of every number.
Step 2: Move to the next integer and check divisibility.
Step 3: List the numbers that divide 4860 completely.
Prime Factors and Prime Factorization
Prime factorization involves dividing 4860 by the smallest prime numbers until you reach 1.
Step 1: Divide 4860 by 2 (smallest prime).
Step 2: Continue dividing by 2 until you can't divide evenly.
Step 3: Move to the next smallest prime, 3, and repeat until you reach 1.
Example Steps: 4860 ÷ 2 = 2430
2430 ÷ 2 = 1215
1215 ÷ 3 = 405
405 ÷ 3 = 135
135 ÷ 3 = 45
45 ÷ 3 = 15
15 ÷ 3 = 5
5 ÷ 5 = 1
Prime Factorization: 4860 = 22× 35× 51 × 71
Factor Tree
A factor tree visually represents the breakdown of 4860 into its prime factors.
This tree shows the breakdown of 4860 into its prime factors : 2, 3, 5, and 7.
Factors of 4860 in Positive and Negative Pairs
Factors can be written in both positive pairs and negative pairs. They are like team members. Their product will equal 4860.
Positive Factor Pairs: (1, 4860), (2, 2430), (3, 1620), ...
Negative Factor Pairs: (-1, -4860), (-2, -2430), (-3, -1620), ...
Common Mistakes and How to Avoid Them in Factors of 4860
Mistakes can occur while finding the factors. Here are common errors and solutions:
Mistake 1
Overlooking larger prime factors.
Ensure that you include all prime numbers up to the square root of 4860 (approximately 69.7).
Factors of 4860 Examples
Problem 1
Can you check whether 75 and 25 are factors of 4860?
Yes, 75 and 25 are factors of 4860
Explanation
To determine whether a number is a factor of another number, divide the larger number by the smaller one. If the remainder is 0, then it is a factor. 4860 ÷ 75 = 64.8 (remainder 0), so 75 is a factor of 4860. 4860 ÷ 25 = 194.4 (remainder 0), so 25 is also a factor of 4860.
Problem 2
Can you find the factors of 4860?
The factors of 4860 are 1, 2, 3, 4, 5, 6, 9, 10, 12, 15, 18, 20, 30, 36, 45, 54, 60, 90, 108, 135, 180, 243, 270, 486, 540, 810, 972, 1620, and 4860.
Explanation
To find the factors of a number, list all whole numbers that divide evenly into it. Start with 1 and continue up to the number itself, checking for a remainder of 0.
Problem 3
Verify whether 4860 is divisible by 3.
Yes, 4860 is divisible by 3.
Explanation
A number is divisible by 3 if the sum of its digits is divisible by 3. For 4860, the sum of the digits is 4 + 8 + 6 + 0 = 18, which is divisible by 3.
Problem 4
Find the greatest common factor (GCF) of 4860 and 75.
The GCF of 4860 and 75 is 15.
Explanation
To find the GCF, list the factors of both numbers and find the largest common factor. Factors of 75: 1, 3, 5, 15, 25, 75 Factors of 4860: 1, 2, 3, 4, 5, 6, 9, 10, 12, 15, 18, 20, 30, 36, 45, 54, 60, 90, 108, 135, 180, 243, 270, 486, 540, 810, 972, 1620, 4860 The common factors are 1, 3, 5, and 15, so the GCF is 15.
Problem 5
Identify the perfect square among the factors of 4860.
The perfect square factor of 4860 is 36 and the root is 6.
Explanation
A perfect square is a number that results from multiplying a number by itself. The factor 36 (6 × 6) is a perfect square, making it the only perfect square factor in the list of factors of 4860.
FAQs on Factors of 4860
1.What are the factors of 4860?
2.How do you determine if a number is a factor of 4860?
3.What is the smallest factor of 4860?
4.What is the largest factor of 4860?
5.How many factors does 4860 have?
6.How many odd factors does 4860 have?
7.What factors go into 4860?
8.Do any perfect squares exist in the factors of 4860?
Important glossaries for the Factors of 4860
- Factors: Numbers that divide a given number completely, without leaving a remainder.
- Prime Factors: Prime numbers that, when multiplied together, result in the given number.
- Prime Factorization: The process of breaking down a number into its prime factors, showing it as a product of prime numbers.
- Factor Tree: A visual tool used to break down a number into its prime factors step by step.
- Perfect Square: A number that is the product of an integer multiplied by itself.
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Hiralee Lalitkumar Makwana
About the Author
Hiralee Lalitkumar Makwana has almost two years of teaching experience. She is a number ninja as she loves numbers. Her interest in numbers can be seen in the way she cracks math puzzles and hidden patterns.
Fun Fact
: She loves to read number jokes and games.
