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2170                                                                 ARITHMETIC

A prime factor is a prime number that is a factor.

4 and   9 are factors of  36

3  and  12   "        "        "   36

2 and  18   "       "       "   36

6 and    6   "       "       "   36 but the prime factors of 36 are 2, 2, 3, and 3.

From this illustration we see that a number may have two or more sets of factors, but there can be only one set of prime factors.

A simple method of finding the prime factors of a number is the following :

2) 36             Divide the given number by the smallest prime number that

2)18      is contained in it without remainder; divide the quotient by the 3)9       smallest prime number that is contained in it without a remain-3        der; and so on until the quotient itself is a prime number.

The several divisors and the last quotient are the prime factors.

A number is divisible by

2 if the units' figure is 2, 4, 6, 8, 0.

3 if the sum of the digits is divisible by 3. 5 if the units' figure is 5 or 0.

9 if the sum of the digits is divisible by 9.

Which of the following numbers are divisible by 2 f by 3 f by 5 f by 9 ? 24         836           516           378           1440           3060

35         225           728           800          1250          3573

63          633           189           297           6744          1620

Find the prime factors of

1.     38:      48:      49:      56:      60:      63:      68:      75:      88:      95

2.     42:      51:      54:    160:    168:    210:    112:    176:    220:    111

3.   252:    234:    225:    208:    329:    357:    208:    192:    476:    102

The factor 2 is found in 8, also in 12, therefore 2 is a common factor of 8 and 12.

The greatest factor common to both 8 and 12 is 4, therefore 4 is the greatest common factor of 8 and 12.

Find the greatest common factor of 24 and 36.

24=2X2X2X3 36=2X2X3X3

The common prime factors are 2, 2, and 3, whose product is 12. Thus 12 is the greatest common factor of 24 and 36.