To find the common factors and common multiples of 70 and 56, we need to first find the prime factorization of both numbers. You have already done that for 70 and 56, so let’s write them down:
70 = 2×5 × 7 56 = 2 × 7
The common factors of 70 and 56 are the numbers that can divide both of them without leaving a remainder. To find them, we need to look at the prime factors that they have in common. In this case, they both have 2 and 7 as prime factors, so we can multiply them to get the common factors. The common factors of 70 and 56 are:
2, 7, and 14
The common multiples of 70 and 56 are the numbers that both of them can divide without leaving a remainder. To find them, we need to look at the least common multiple (LCM) of 70 and 56, which is the smallest number that both of them can divide. To find the LCM, we need to multiply the highest power of each prime factor that appears in either number. In this case, we have:
LCM(70, 56) = 2×5 × 7 = 280
The common multiples of 70 and 56 are then the multiples of the LCM, which are:
280, 560, and 840
I hope this helps you understand how to find the common factors and common multiples of two numbers.