What is 1029 divisible by?

Answer 1

3, 7, 21, 49, 147, 343

How to find the answer

We need to check for divisibility with numbers up to the square root of 1029, which is 32.xx. So we need to check divisibility by prime numbers up to 32.

2: 1029 is not an even number, so 1029 is not divisible by 2.

3: The test of divisibility by 3 is to add the digits. 1+0+2+9 = 12, so 1029 is divisible by 3. Dividing 1029 by 3 gives 343. The square root of 343 is 18.xx.

5: 343 is not even or divisible by 3; it does not end in a 5 or a 0, so 343 is not divisible by 5.

7: Split up the number into the last digit and everything else: 34 and 3. Multiply the last number by 2 and take that off the first: 34-2x3=34-6=28. Since 28 is divisible by 7, 343 is also divisible by 7. Dividing 343 by 7, we get 49, which we recognize as 7x7. So 343 is 7 cubed.

8. So the prime factors of 1029 are 3 and 7. 1029=3x73. The divisors are 3, 7, 72=49, 73=343, and 3x7=21, and 3x49=147.

So the divisors are 3, 343, 7, 147, 21, and 49.