Factors of a number are the integers that divide it completely without leaving any remainder. In this explanation, we will determine the factors of 74, identify its pair factors, find its prime factorization, and represent it using a factor tree. Let’s dive into the detailed steps.
What Are the Factors of 74?
To find the factors of 74, we divide it by integers starting from 1 up to 74 and check which numbers leave no remainder.
1 × 74 = 74
2 × 37 = 74
Thus, the factors of 74 are: 1, 2, 37, 74.
Pair Factors of 74
Pair factors are the pairs of numbers that multiply to give 74. Let’s find them:
1 × 74 = 74
2 × 37 = 74
Pair Factors: (1, 74) and (2, 37)
For negative pair factors:
(-1, -74) and (-2, -37) also work because the product of two negative numbers is positive.
Prime Factorization of 74
Prime factorization involves breaking the number down into its prime factors:
Start with the smallest prime number, 2.
74 ÷ 2 = 37 (since 74 is even, it’s divisible by 2).
Next, check if 37 is prime. It is, as it’s not divisible by any number other than 1 and 37.
Prime Factorization of 74: 2 × 37
Factor Tree of 74
The factor tree represents the prime factorization visually. For 74:
Start with 74 at the top.
Split 74 into 2 × 37.
Both 2 and 37 are prime numbers, so the tree ends there.
74
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2 37