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.
