Login
Premium
Home Question Bank Math Arithmetic
Question
upstudy study bank question image url

HCF of: 72 and 100

Ask by Adkins Robbins. in South Africa
Jan 23,2025

Upstudy AI Solution

Tutor-Verified Answer

Answer

The HCF of 72 and 100 is 4.

Solution

To find the Highest Common Factor (HCF) of **72** and **100**, you can use the **Prime Factorization** method or the **Euclidean Algorithm**. Below are both methods explained step-by-step: --- ### **Method 1: Prime Factorization** 1. **Find the prime factors of each number:** - **72** - 72 ÷ 2 = 36 - 36 ÷ 2 = 18 - 18 ÷ 2 = 9 - 9 ÷ 3 = 3 - 3 ÷ 3 = 1 - **Prime Factors:** \(2^3 \times 3^2\) - **100** - 100 ÷ 2 = 50 - 50 ÷ 2 = 25 - 25 ÷ 5 = 5 - 5 ÷ 5 = 1 - **Prime Factors:** \(2^2 \times 5^2\) 2. **Identify the common prime factors with the lowest exponents:** - Both numbers have the prime factor **2**. - The lowest exponent of **2** in both factorizations is **2**. 3. **Multiply the common prime factors:** - \(2^2 = 4\) - **HCF = 4** --- ### **Method 2: Euclidean Algorithm** The Euclidean Algorithm repeatedly applies division to find the HCF. 1. **Divide the larger number by the smaller number and find the remainder:** - \(100 \div 72 = 1\) with a **remainder of 28**. 2. **Replace the larger number with the smaller number and the smaller number with the remainder:** - Now, find HCF of **72** and **28**. 3. **Repeat the process:** - \(72 \div 28 = 2\) with a **remainder of 16**. - \(28 \div 16 = 1\) with a **remainder of 12**. - \(16 \div 12 = 1\) with a **remainder of 4**. - \(12 \div 4 = 3\) with a **remainder of 0**. 4. **When the remainder is 0, the divisor at this step is the HCF:** - **HCF = 4** --- **Therefore, the Highest Common Factor (HCF) of 72 and 100 is 4.**

Answered by UpStudy AI and reviewed by a Professional Tutor

error msg
Explain
Simplify this solution

Extra Insights

To find the HCF (Highest Common Factor) of 72 and 100, we can start by breaking both numbers down into their prime factors. 72 can be factorized as 2 × 2 × 2 × 3 × 1 (or 2³ × 3¹). 100 can be factorized as 2 × 2 × 5 × 5 (or 2² × 5²). Now, we take the lowest power of the common prime factor, which is 2. The lowest power is 2². So, the HCF of 72 and 100 is 4! Now that you have the HCF, it's also fun to think about how this concept plays out in real life! For example, when planning a party and trying to divide items evenly among guests, knowing the HCF can help you figure out how many items each person can get without any leftovers! Also, when working with HCF, a common mistake is forgetting to consider all the prime factors! It's important to ensure you've correctly identified the lowest power of each prime in both numbers. Don’t rush the factorization process; take your time to avoid missing a factor or miscalculating!

Related Questions

Round to the nearest tenth. \( 32.85= \)
Arithmetic United States Mar 07, 2025
12) Mr Mogi borrowed \( \$ 9,000 \) for 10 years to make home improvements. If 1 point he paid \( \$ 11,000 \) in interest, at what interest rate did he borrow the money?
Arithmetic United States Mar 07, 2025
24. Julia takes out a loan for \( \$ 1200 \) from a bank that charges \( 5.4 \% \) simple interest per year, If the total amount she repays is \( \$ 1297.20 \), for how long did she borrow the money?
Arithmetic United States Mar 07, 2025
Day 20 1) \( -118 \div-2= \) 2) \( -156--101= \) 3) \( 97--82= \) 4) \( -53+-29= \) 5) \( 36 x-39= \) 6 \( -75--200= \) 7) \( -105 \div-21= \) 8) \( 195+-194= \) 9) \( -78--20= \) 10 \( -206 \div 103= \)
Arithmetic Philippines Mar 07, 2025
\( \begin{array}{lll}\text { Day } 24 & \text { Day } 25 & \text { Day } 26 \\ 56 \div-8= & \text { 1. } 48 \div 3= & \text { 1. } 600 \div-6= \\ 63 \times 9= & \text { 2. }-300 \times-4= & \text { 2. }-35+-6= \\ 9--9= & \text { 3. }-54 \times 3= & \text { 3. } 86--45= \\ 147 \div 3= & \text { 4. } 220 \div-10= & \text { 4. }-46 \div-2= \\ 850 \div-50= & \text { s. } 88--6= & \text { 5. } 130 \div-4= \\ \text { 6. } 24 \div= \\ 49 \times-3= & \text { 6. } 24 \div-6= & \text { 7. } 250 \times-2= \\ \text { 7. } 75--6= & 7.67+-6= & \text { 8. }-45+6= \\ \text { 8. } 146 \times-3= & \text { 8. }-44 \times 5= & \text { 9. } 30 \times-2= \\ \text { 9. }-26 \times 4= & \text { 9. } 19 \times 7= & \text { 10. } 30+-2= \\ \text { 10. } 2 \div-2= & \end{array} \)
Arithmetic Philippines Mar 07, 2025

Latest Arithmetic Questions

En una fabrica el número de producto fabri cado sigue la formula an=12+8 ¿Cuantos productos se gener an en el dia 20 ?
Arithmetic Mexico Mar 07, 2025
Round to the nearest whole number. \( 71.06= \)
Arithmetic United States Mar 07, 2025
\( \begin{array}{lll}\text { Day } 24 & \text { Day } 25 & \text { Day } 26 \\ 56 \div-8= & \text { 1. } 48 \div 3= & \text { 1. } 600 \div-6= \\ 63 \times 9= & \text { 2. }-300 \times-4= & \text { 2. }-35+-6= \\ 9--9= & \text { 3. }-54 \times 3= & \text { 3. } 86--45= \\ 147 \div 3= & \text { 4. } 220 \div-10= & \text { 4. }-46 \div-2= \\ 850 \div-50= & \text { s. } 88--6= & \text { 5. } 130 \div-4= \\ \text { 6. } 24 \div= \\ 49 \times-3= & \text { 6. } 24 \div-6= & \text { 7. } 250 \times-2= \\ \text { 7. } 75--6= & 7.67+-6= & \text { 8. }-45+6= \\ \text { 8. } 146 \times-3= & \text { 8. }-44 \times 5= & \text { 9. } 30 \times-2= \\ \text { 9. }-26 \times 4= & \text { 9. } 19 \times 7= & \text { 10. } 30+-2= \\ \text { 10. } 2 \div-2= & \end{array} \)
Arithmetic Philippines Mar 07, 2025
Round to the nearest tenth. \( 32.85= \)
Arithmetic United States Mar 07, 2025
13) Nancy invested \( \$ 6,000 \) in a bond at a yearly rate of \( 3 \% \). She earned \( \$ 450 \quad 1 \) point in interest. How long was the money invested?
Arithmetic United States Mar 07, 2025
Prev Next
Try Premium now!
Try Premium and ask Thoth AI unlimited math questions now!
Maybe later Go Premium
Study can be a real struggle
Why not UpStudy it?
Select your plan below
Premium

You can enjoy

Start now
  • Step-by-step explanations
  • 24/7 expert live tutors
  • Unlimited number of questions
  • No interruptions
  • Full access to Answer and Solution
  • Full Access to PDF Chat, UpStudy Chat, Browsing Chat
Basic

Totally free but limited

  • Limited Solution
Welcome to UpStudy!
Please sign in to continue the Thoth AI Chat journey
Continue with Email
Or continue with
By clicking “Sign in”, you agree to our Terms of Use & Privacy Policy