Find HCF and LCM
I track all of my science test score this year. Calculate the average .Here are my science test score
80,90,95,72,83,100,94
add 'em up and divide by 7
To find the Highest Common Factor (HCF) and Lowest Common Multiple (LCM) of a set of numbers, you can follow these steps:
Step 1: Write down the given numbers: 80, 90, 95, 72, 83, 100, 94.
Step 2: To find the HCF, identify the largest factor that divides all the given numbers evenly. Start by finding the factors of the largest number (in this case, 100) and check if it is a factor of all the other numbers. Repeat this process, considering smaller factors until you find the largest common factor.
- Factors of 100: 1, 2, 4, 5, 10, 20, 25, 50, 100
- Factors of 94: 1, 2, 47, 94
- Factors of 95: 1, 5, 19, 95
- Factors of 83: 1, 83
- Factors of 72: 1, 2, 3, 4, 6, 8, 9, 12, 18, 24, 36, 72
- Factors of 90: 1, 2, 3, 5, 6, 9, 10, 15, 18, 30, 45, 90
- Factors of 80: 1, 2, 4, 5, 8, 10, 16, 20, 40, 80
From the above factors, the highest common factor is 1, as it is the only factor that is common to all the given numbers.
So, the HCF of the given numbers is 1.
Step 3: To find the LCM, you need to identify the smallest number that is divisible by all the given numbers. Start with the largest number (100) and keep multiplying it by different numbers until you find the smallest common multiple.
LCM = (100 * 1) = 100
LCM = (100 * 2) = 200
LCM = (100 * 3) = 300
LCM = (100 * 4) = 400
LCM = (100 * 5) = 500
LCM = (100 * 6) = 600
LCM = (100 * 7) = 700
LCM = (100 * 8) = 800
LCM = (100 * 9) = 900
LCM = (100 * 10) = 1000
From the above calculations, the LCM of the given numbers is 1000.
So, the HCF is 1 and the LCM is 1000.
To find the HCF (Highest Common Factor) and LCM (Least Common Multiple), we need to find the factors of the given numbers.
The given numbers are: 80, 90, 95, 72, 83, 100, 94.
To find the HCF:
Step 1: List the prime factors of each number:
- 80 = 2 * 2 * 2 * 2 * 5 = 2^4 * 5
- 90 = 2 * 3 * 3 * 5 = 2 * 3^2 * 5
- 95 = 5 * 19
- 72 = 2 * 2 * 2 * 3 * 3 = 2^3 * 3^2
- 83 = 83
- 100 = 2 * 2 * 5 * 5 = 2^2 * 5^2
- 94 = 2 * 47
Step 2: Identify the common factors.
The prime factors common to all the numbers are: 2.
Step 3: Multiply the common factors:
HCF = 2.
To find the LCM:
Step 1: List the prime factors of each number.
- 80 = 2^4 * 5
- 90 = 2 * 3^2 * 5
- 95 = 5 * 19
- 72 = 2^3 * 3^2
- 83 = 83
- 100 = 2^2 * 5^2
- 94 = 2 * 47
Step 2: Identify the highest exponent for each prime factor.
The highest exponents for each prime factor are:
2: 4 (from 80 and 72), 5 (from 100), 1 (from 90 and 94)
3: 2 (from 72), 1 (from 90)
5: 1 (from 80 and 90), 2 (from 100)
19: 1 (from 95)
47: 1 (from 94)
83: 1 (from 83)
Step 3: Multiply the prime factors with their highest exponents:
LCM = 2^4 * 3^2 * 5^2 * 19 * 47 * 83
Therefore, the HCF is 2 and the LCM is 112,332,600.
Now, to calculate the average of the science test scores:
Add up all the test scores: 80 + 90 + 95 + 72 + 83 + 100 + 94 = 614.
Divide the sum by the number of scores (7 in this case) to find the average:
Average = 614 / 7 = 87.71 (rounded to two decimal places).
So, the average of the science test scores is approximately 87.71.