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We are given:
HCF = 12
LCM = 336
One number = 84
We are to find the other number.
🧠 Concept:
We use the fundamental relation between two numbers, their HCF and LCM:
HCF×LCM=Product of the two numbers\text{HCF} × \text{LCM} = \text{Product of the two numbers}
🔢 Step-by-step Calculation:
Let the other number be x.
We are given:
12×336=84×x12 × 336 = 84 × x 4032=84×x4032 = 84 × x
Now solve for x:
x=403284=48x = \frac{4032}{84} = 48
✅ Final Answer:
The other number is 48.
🧪 Check (optional):
HCF of 84 and 48 = 12
LCM of 84 and 48 = (84 × 48) / 12 = 4032 / 12 = 336 ✅
Hence, correct!
To find the HCF (Highest Common Factor) of 0.54, 1.8, and 7.2, follow these steps:
🟠 Step 1: Convert all decimals to whole numbers
To eliminate decimals, multiply each number by 100 (to make them whole):
0.54 × 100 = 54
1.8 × 100 = 180
7.2 × 100 = 720
So now we need to find the HCF of 54, 180, and 720.
🟠 Step 2: Prime factorization
54 = 2 × 3³
180 = 2² × 3² × 5
720 = 2⁴ × 3² × 5
Common prime factors:
2 (minimum power is 1)
3 (minimum power is 2)
So, HCF = 2 × 3² = 2 × 9 = 18
But remember, we multiplied each number by 100, so we must divide the result by 100 to bring it back to the original scale.
🟢 Step 3: Convert HCF back to decimal
18 ÷ 100 = 0.18
✅ Final Answer:
The H.C.F. of 0.54, 1.8, and 7.2 is 0.18