Last updated on May 26th, 2025
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.
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.
Factors help us divide numbers equally, making calculations faster and easier. Given below are the methods used to find factors:
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.
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.
The breaking down of numbers as prime factors is called prime factorization. The factors of 630 are:
630=2 × 32 × 5 x7
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
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)
While learning about factors of 630, students may likely make mistakes, to avoid a few mistakes solutions are given below:
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
The total number of factors is 24 because this formula considers every possible combination of the prime factors.
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
The GCF of 630 and 315 is 315 because it is the largest number that divides both 630 and 315 without any remainder.
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
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.