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Factors and multiples
For example, let’s compare 1,469 and 1,463. Since the number of digits in both numbers are the same (that is 4), we must compare the digits from the left. Now 1, 4 and 6 are common among both numbers from the left. The unequal digits are 9 & 3 and since 9 is the greater number of the two, 1,469 is greater than 1,463.
II. Factors & Multiples
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To understand factors & multiples, we must first know the concept of divisibility. Make sure to practise your knowledge of division at Takshila Learning.
II.I Factors
Now, if a number (dividend) is exactly divided by any number (divisor), the divisor is a factor of that dividend. For example, when we divide 100 (dividend) by 5 (divisor), it leaves no remainder and divides completely with 20 being the quotient. Thus we can say that 5 is a factor.
If you notice carefully, even 20 is a factor because even it can divide 100 completely, leaving no remainder and quotient as 5. Thus we can say that for any number which is divided into another number and leaves no remainder, then both the divisor and the quotient is a factor of the dividend.
To put it another way, When a number is considered to be a factor of another number, it means that the first number must entirely divide the second number, leaving no remainder.
Now a fun thing to notice here! Each number has 1 as a common component since we can divide all numbers by 1. Therefore, 1 is a factor for all numbers.
Another fun thing to notice is that each number is a factor of itself since every number will divide itself completely. For example, 20 is divisible by 20. Therefore, 20 is a factor of itself!
Similarly, when we divide 30 by 5, it leaves no remainder and the quotient becomes 6. Thus we can say that 5, 30 and 1 are factors of 30.
II.II Multiples
A multiple of a number is the result of multiplying a given integer by another natural number. For example, multiples of 2 are 2 (2X1), 4 (2X2), 6 (2X3), 8 (2X4), etc.
A quick tip to keep in mind is that whenever we need to calculate multiples, we can simply come up with the table of those particular numbers and calculate multiples.
