Factor and Multiple

1. Find all the possible values of the digits X and Y if the six-digit number 123X4Y is divisible by 4 and 9 ?

2. Given a six-digit number 568XYZ, find the values of X, Y and Z such that the number is divisible by 3, 4 and 5 and is also the smallest six-digit number starting with 568 ?

3. Find the sum of first three prime numbers that end with a 9 ?

4. Paul has three pieces of rope with lengths of 140 cm, 168 cm and 210 cm. He wishes to cut the three pieces of rope into smaller pieces of equal length with no remainders.
What is greatest possible length of each of the smaller pieces of rope ?
How many of the smaller pieces of rope of equal length can he get ?

5. Two lighthouses flash their lights every 20 seconds and 30 seconds respectively. Give that they flash together at 8 p.m., when will they next flash together again ?

6. John , Peter and Paul were each given a piece of string of equal length. John cut his into equal lengths of 2 m; Peter cut his into equal lengths of 3 m; and Paul cut his into equal lengths of 5 m. If there was no remainder in each case, find the shortest length of string given to each of them.

7. Find the two number if their LCM is 120 and their HCF is 4. (Given three possible answers.)

8. Using prime factorization, find the square root of 148,225 ?

9. Using prime factorization, find the cube root of 74,088 ?

10. Insert +, -, X, : and brackets to make the following sentences true
5 5 5 5 5 5 = 7