195 LearnersLast updated on May 26th, 2025
Factors of 630
Factors are the numbers that divide another number equally, without leaving any remainder. When you multiply two numbers to find another number, the two which are multiplied are factors. You can think of factors as the building blocks that will help you make numbers.
What are the factors of 630?
Factors are the numbers that help us divide things equally without any leftovers. The numbers 1, 2, 3, 5, 6, 7, 9, 10, 14, 15, 18, 21, 30, 35, 42, 63, 70, 105, 126, 210, and 630 are the factors of 630. The number has both positive and negative integers that divide 630 without leaving any remainder.
How to find the factors of 630?
Factors help us divide numbers equally, making calculations faster and easier. Given below are the methods used to find factors:
Multiplication Method
In this method, we take two numbers and find the product of those two numbers to get the required number.
Example:
2×315=630
1×630=630 and so on,
This means that 1, 2, 3, 5, 6, 7, 9, 10, 14, 15, 18, 21, 30, 35, 42, 63, 70, 105, 126, 210, and 630 are the factors of 630.
Division Method
We divide 630 by numbers starting from 1 and see which number gives the remainder of 0.
630 ÷ 1=630
630 ÷ 2=315
630 ÷ 3=210
630 ÷ 5=126
630 ÷6=105
630 ÷ 7=90
630 ÷9=70
630 ÷10=63
And continuing until you get 1. So the factors are 1, 2, 3, 5, 6, 7, 9, 10, 14, 15, 18, 21, 30, 35, 42, 63, 70, 105, 126, 210, and 630.
Prime Factorization
The breaking down of numbers as prime factors is called prime factorization. The factors of 630 are:
630=2 × 32 × 5 x7
Factor tree
A factor tree shows how a number can be parted down into prime factors.630 is broken down into two factors, 2,3,5 and 7
Factor pair
Positive and negative pairs:
The factors of a number will have both the positive and negative numbers:
Positive :( 1, 2, 3, 5, 6, 7, 9, 10, 14, 15, 18, 21, 30, 35, 42, 63, 70, 105, 126, 210, and 630)
Negative:(-1,- 2,- 3,- 5,- 6,- 7,- 9, -10,- 14,- 15, -18, -21, -30, -35,- 42,- 63,- 70,- 105, -126, -210, and -630)
Common Mistakes and How to Avoid Them in Factors of 630
While learning about factors of 630, students may likely make mistakes, to avoid a few mistakes solutions are given below:
Mistake 1
Improper calculation in division
Children may get confused while performing divisions in the carry forward of numbers, which may lead to improper results. To avoid this, students should practice division to be better at the calculations.
factors of 630 Examples
Problem 1
How many total factors does 630 have?
Using Prime Factorization:
630=2×32×5×7
Calculate the Number of Factors:
(1+1)(2+1)(1+1)(1+1)=2×3×2×2=24
Total Number of Factors=24
Explanation
The total number of factors is 24 because this formula considers every possible combination of the prime factors.
Problem 2
What is the greatest common factor (GCF) of 630 and 315?
Prime Factorization:
630=2×32×5×7
315=32×5×7
Identify Common Factors:
Minimum exponent for each prime:
For 3: 2
For 5: 1
For 7: 1
Calculate GCF:
GCF=32×5×7=315
Explanation
The GCF of 630 and 315 is 315 because it is the largest number that divides both 630 and 315 without any remainder.
Problem 3
What is the largest factor of 630 that is less than 300?
1. List Factors of 630: 1,2,3,5,6,7,9,10,14,15,18,21,30,35,42,63,70,105,126,210,630
2. Identify Largest Factor Less Than 300: Largest Factor=210
Explanation
210 is the largest factor of 630 which is less than 300, as it is the highest number in the factors list that satisfies the condition.
FAQs on Factors of 630
1.What is the negative pair of 630?
2.Is 630 a natural number?
3.Is 630 a perfect square?
4.What number is the factor of 216 and 630?
5.How can children in Thailand use numbers in everyday life to understand Factors of 630?
6.What are some fun ways kids in Thailand can practice Factors of 630 with numbers?
7.What role do numbers and Factors of 630 play in helping children in Thailand develop problem-solving skills?
8.How can families in Thailand create number-rich environments to improve Factors of 630 skills?
Necessary Glossaries for factors of 630
- Prime Factorization: The breaking down of numbers as prime factors is called prime factorization. For example:630=2 × 32 × 5 x7
- Divisibility: A number is said to be divisible by a certain number, when we divide a number it should give a whole number and not a decimal.
- Even number: A number that when divided by 2 gives a whole number.
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