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Demonstration : ## What are the multiples of 29?

The first 20 multiples of 29 greater than 0 are: 29 ; 58 ; 87 ; 116 ; 145 ; 174 ; 203 ; 232 ; 261 ; 290 ; 319 ; 348 ; 377 ; 406 ; 435 ; 464 ; 493 ; 522 ; 551 ; 580.
If a positive integer is a multiple of 29 we can divide it by 29 to find an integer quotient and zero remainder. We can also multiply 29 by another positive integer to get it (the multiple of 29).
If a whole number is a multiple of 29 we say it is divisible by 29 or 29 divides the whole number (29 is its divisor or its factor).
Example: Let's verify if 87 is a multiple of 29.
By dividing 87 by 29 we get 3 as integer quotient and the remainder of the division is equal to zero. 29 multiplied by 3 gives 87. Those two arithmetic operations (the multiplication and the division) show that 87 is a multiple of 29 because 87 divided by 29 gives an integer quotient and zero remainder, and the product of 29 and 3 is equal to 87.
Remark:
29 is a prime number, if the decomposition into product of prime factors of an integer contains 29 then that integer is a multiple of 29.
Since 29 is an odd number its multiples are positive integers that are odd numbers or even numbers. All positive integers have an infinite number of multiples, so does 29.
Here are some multiples of 29 greater than 0:
Multiples of 29 less than 1000:
29; 58; 87; 116; 145; 174; 203; 232; 261; 290; 319; 348; 377; 406; 435; 464; 493; 522; 551; 580; 609; 638; 667; 696; 725; 754; 783; 812; 841; 870; 899; 928; 957; 986.

Multiples of 29 up to 1000 and less than 2000:
1015; 1044; 1073; 1102; 1131; 1160; 1189; 1218; 1247; 1276; 1305; 1334; 1363; 1392; 1421; 1450; 1479; 1508; 1537; 1566; 1595; 1624; 1653; 1682; 1711; 1740; 1769; 1798; 1827; 1856; 1885; 1914; 1943; 1972.

Multiples of 29 between 2000 and 3000:
2001; 2030; 2059; 2088; 2117; 2146; 2175; 2204; 2233; 2262; 2291; 2320; 2349; 2378; 2407; 2436; 2465; 2494; 2523; 2552; 2581; 2610; 2639; 2668; 2697; 2726; 2755; 2784; 2813; 2842; 2871; 2900; 2929; 2958; 2987.

Multiples of 29 up to 4000 and less than 5000:
4002; 4031; 4060; 4089; 4118; 4147; 4176; 4205; 4234; 4263; 4292; 4321; 4350; 4379; 4408; 4437; 4466; 4495; 4524; 4553; 4582; 4611; 4640; 4669; 4698; 4727; 4756; 4785; 4814; 4843; 4872; 4901; 4930; 4959; 4988.

Is 29 a multiple of 3?
29 is not a multiple of 3 because 29 is a prime number and has only two divisors: 1 and 29. Since 3 is not a divisor of 29 then 29 is not a multiple of 3.

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