Numbers like 10 and 36 and 49 that can be composed as products of smaller counting numbers are called composite numbers. Prime and composite numbers: We can build 36 from 9 and 4 by multiplying or we can build it from 6 and 6 or from 18 and 2 or even by multiplying 2 × 2 × 3 × 3. But only some counting numbers can be composed by multiplying two or more smaller counting numbers. Doing so will allow you to quickly see that 61 and 67 are not multiples of a given single-digit number, such as 7.Building numbers from smaller building blocks: Any counting number, other than 1, can be built by adding two or more smaller counting numbers. If you have trouble seeing that 61 and 67 are prime, I would suggest that you review your multiplication tables. In other words, if you have a two-digit number that is not divisible by 2, 3, 5 and 7, it must be a prime. That is, it can’t be divisible by 2, 3, 5 and 7. Here is a useful rule: If a two-digit number is a prime, it can’t be divisible by any of the single-digit primes. They are not, and therefore they must be both prime. Thus, we can eliminate 63 and 69 from the list because they are not prime.įinally, we are left with 61 and 67, and we must determine whether they are divisible by 7. We see that 60, 63, 66, 69 are all multiples of 3 and therefore are not prime. If you don’t know an easy way to do this, just start with a number that is an obvious multiple of 3, such as 60, and then keep adding 3. To eliminate any remaining values, we would look at those that are multiples of 3. We can next eliminate 65 because 65 is a multiple of 5. Immediately we can eliminate the EVEN NUMBERS because they are divisible by 2 and thus are not prime. Therefore, a prime number is divisible by two numbers only.
![list of prime numbers to 30 list of prime numbers to 30](https://cdn.numerade.com/previews/5909cfa6-3815-4288-8cc7-2602ebf4226f.gif)
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The sum of prime numbers that are greater than 60 but less than 70 isĪ prime number is a number that has only two factors: 1 and itself. Therefore the only 2 primes in the set are 61 and 67.ĭoes anyone know a good way to check for divisibility by 7? Thanks. This does not work when applied to 61 or 67 and is redundant for 63 (we knocked 63 out in the "For 3" rule). Since neither 61 nor 67 is even, 8 cannot be a divisor.įor 9: Add up all the digits and see if the resulting sum is divisible by 9. You know 2 is a prime factor of 8 meaning any number that has 8 as a multiple must be even. I didn't stick to this rule when using the divisibility rules approach. Does anyone know a quick way to check for divisibility by7? Regardless, you can run through the multiples of 7 and realize none fall on 61 or 67 so this divisor doesn't check out.įor 8: If the last 3 digits are divisible by 8, then the whole number is divisible by 8. I recommend long-division or mental math. This does not apply to 61 and 67 since neither is divisible by 2 or 3.įor 7: No concise rule that I know of. This eliminates 65, leaving only 61 and 67 in the running for primes.įor 6: If the number is divisible by BOTH 2 & 3 (see first two rules), then the number is also divisible by 6.
![list of prime numbers to 30 list of prime numbers to 30](https://i.ytimg.com/vi/RQW8e-LJTvI/maxresdefault.jpg)
This does not apply to any of our remaining numbers - 61, 65, and 67.įor 5: All numbers ending in 5 or 0. This eliminates both 63 and 69.įor 4: If the last 2 digits of the number are divisible by 4, the entire number is divisible by 4. If the sum is divisible by 3, the number is divisible by 3. This eliminates 62, 64, 66, and 68.įor 3: Add up all the digits of the number. The second way - applying divisibility rules - seems more elegant and more efficient in the long run:įor 2: All even numbers. That leaves you with 2 primes - 61 and 67 - the sum of which is 128. 63 and 69 are divisible by 9 and 3 respectively (just plug and chug). You know the even numbers - 62, 64, 66, and 68 will never be prime.
![list of prime numbers to 30 list of prime numbers to 30](https://doubtnut-static.s.llnwi.net/static/ss/web/113696.jpg)
The first way used a combination of pure processing power and logic.