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 help us divide numbers equally, making calculations faster and easier. We can find factors from the following methods:
We divide 560 by numbers starting from 1 and see which number gives the remainder of 0.
560 ÷ 1=560
560 ÷2=280
560 ÷4=140
560 ÷8=70
So the factors are 1, 2, 4, 5, 7, 8, 10, 14, 16, 20, 28, 35, 40, 56, 70, 80, 112, 140, 280, 560.
The breaking down of numbers as prime factors is called prime factorization. The factors of 560 are:
560=24 x 5 × 7
A factor tree shows how a number can be parted down into prime factors.560 is broken down into two factors, Start with 560, and break it into 2 and 280.
280 splits into 2 and 140, then 140 into 2 and 70.
Continue until only prime numbers are left: 2, 2, 2, 2, 5, 7.
Positive and negative pairs:
The factors of a number will have both the positive and negative numbers:
Positive pairs: (1, 560), (2, 280), (4, 140), (5, 112), (7, 80), (8, 70), (10, 56), (14, 40), (16, 35), (20, 28)
Negative pairs: (-1, -560), (-2, -280), (-4, -140), (-5, -112), (-7, -80), (-8, -70), (-10, -56), (-14, -40), (-16, -35), (-20, -28)
While learning about factors of 560, students may likely make mistakes, to avoid them a few mistakes with solutions are given below:
Verify if 560 is divisible by 12.
For a number to be divisible by 12, it must be divisible by both 3 and 4.
Sum of digits: 5+6+0=115 + 6 + 0 = 115+6+0=11 → Not divisible by 3.
560÷4=140 → Divisible by 4.
560 is not divisible by 3, it is not divisible by 12.
What is the least common multiple (LCM) of 560 and 70?
560 = 24 × 5 × 7,
70= 2 × 5 × 7
LCM= 2 4 × 5 × 7=560.
The LCM of 560 and 70 is 560.
Find the GCF of 560 and 168.
Factors of 560:1,2,4,…,560
Factors of 168: 1,2,4,…,168
The largest common factor is 56.
GCF(560, 168) = 56
The largest factor common to both numbers is 56.