How Do You Find The HCF Of 867 And 255?
The HCF of 867 and 255 is 51, found by identifying the greatest common divisor through prime factorization or the Euclidean algorithm.
Prime factors of 867? That’s 3 × 17 × 17. For 255, you get 3 × 5 × 17. Now look at what they share: both have 3 and 17. Multiply those common factors (3 × 17) and you get 51. Alternatively, use Euclid’s division trick—keep subtracting the smaller number from the larger until you hit zero. The last non-zero remainder? That’s your HCF. Honestly, this is the best approach for most cases.
What is the HCF of 867 and 225?
The HCF of 867 and 225 is 3.
Start with the bigger number, 867, and divide it by 225. You get 3 with a remainder of 192. Next, take 225 and divide by 192—remainder 33 pops up. Then divide 192 by 33, which leaves 27. Keep going until the remainder vanishes. The last non-zero remainder? That’s 3, your HCF. (If you’re wondering, this is why Euclid’s method works so well—it shrinks the problem fast.)
What is Euclid’s method to find HCF?
Euclid’s method uses division with remainders to find the HCF of two numbers by repeatedly replacing the larger number with the remainder until the remainder is zero.
Here’s how it works: divide the bigger number by the smaller, note the remainder, then repeat with the smaller number and that remainder. Rinse and repeat. For 867 and 255, you’d do 867 ÷ 255 = 3 with remainder 102. Then 255 ÷ 102 = 2 with remainder 51. Finally, 102 ÷ 51 = 2 with remainder 0. The HCF? 51. This isn’t just math—it’s the backbone of the Euclidean algorithm, used everywhere from cryptography to computer science because it’s simple and lightning-fast.
What is the HCF of 865 and 225?
The HCF of 865 and 225 is 5.
Fire up Euclid’s algorithm: 865 ÷ 225 = 3, remainder 190. Next, 225 ÷ 190 = 1, remainder 35. Then 190 ÷ 35 = 5, remainder 15. Finally, 35 ÷ 15 = 2, remainder 5. One more step: 15 ÷ 5 = 3, remainder 0. The last non-zero remainder is 5, so that’s your HCF. Or check prime factors—5 is the only one they share. Either way, you land on 5.
How do you find the HCF of a function?
To find the HCF of a function, determine the greatest common divisor of the coefficients by using the Euclidean algorithm on the numerical values.
Take two linear functions, say f(x) = 6x + 9 and g(x) = 15x + 21. Focus on the numbers: 6, 9 and 15, 21. Run Euclid’s algorithm on 9 and 15: 15 ÷ 9 = 1 remainder 6; 9 ÷ 6 = 1 remainder 3; 6 ÷ 3 = 2 remainder 0. The HCF of the coefficients is 3, so the HCF of the functions is 3. This trick works for polynomials too—just look at their numerical coefficients.
What is the HCF of 1620, 1725 and 255?
The HCF of 1620, 1725, and 255 is 15.
First, find the HCF of 1620 and 255. 1620 ÷ 255 = 6 remainder 90. Then 255 ÷ 90 = 2 remainder 75. Next, 90 ÷ 75 = 1 remainder 15. Finally, 75 ÷ 15 = 5 remainder 0. So HCF(1620, 255) = 15. Now check 15 against 1725: 1725 ÷ 15 = 115 with zero remainder. The HCF stays 15. That means 15 is the largest number that divides all three evenly. Not bad for a few quick steps.
What is the HCF of 240 and 228?
The HCF of 240 and 228 is 12.
Euclid’s algorithm saves the day again: 240 ÷ 228 = 1 remainder 12. Then 228 ÷ 12 = 19 remainder 0. The last non-zero remainder is 12. Want to double-check? List the factors. 228 has 1, 2, 3, 4, 6, 12, 19, 38, 57, 76, 114, 228. 240 has 1, 2, 3, 4, 5, 6, 8, 10, 12, 15, 16, 20, 24, 30, 40, 48, 60, 80, 120, 240. The highest common one? Yep, 12.
What is the HCF of 96 and 404?
The HCF of 96 and 404 is 4.
Start with 404 ÷ 96 = 4 remainder 20. Next, 96 ÷ 20 = 4 remainder 16. Then 20 ÷ 16 = 1 remainder 4. Finally, 16 ÷ 4 = 4 remainder 0. The HCF is 4. Check prime factors to confirm: 96 = 2⁵ × 3 and 404 = 2² × 101. The common part? 2² = 4. Simple as that.
What is the HCF of 1260 and 7344?
The HCF of 1260 and 7344 is 36.
Euclid’s algorithm in action: 7344 ÷ 1260 = 5 remainder 1044. Then 1260 ÷ 1044 = 1 remainder 216. Next, 1044 ÷ 216 = 4 remainder 180. Then 216 ÷ 180 = 1 remainder 36. Finally, 180 ÷ 36 = 5 remainder 0. The HCF is 36. Or try prime factorization: 1260 = 2² × 3² × 5 × 7 and 7344 = 2³ × 3² × 102. The overlap? 2² × 3² = 36. Solid.
What is HCF formula?
The HCF of numbers x, y, and z is the largest integer that divides all three without a remainder, and it can be calculated using the Euclidean algorithm or prime factorization.
For three numbers, find the HCF of two first, then pair that result with the third. Example: HCF(24, 36, 60). First, HCF(24, 36) = 12. Then HCF(12, 60) = 12. The HCF pops up everywhere—simplifying fractions, finding common denominators, even in number theory puzzles. It’s one of those math tools you’ll use more than you think.
What is the HCF of 16 and 24?
The HCF of 16 and 24 is 8.
List the factors. 16 gives you 1, 2, 4, 8, 16. 24 gives 1, 2, 3, 4, 6, 8, 12, 24. The biggest number in both lists? 8. Euclid’s method: 24 ÷ 16 = 1 remainder 8; 16 ÷ 8 = 2 remainder 0. The HCF is 8. Handy for simplifying fractions—like turning 16/24 into 2/3.
What is the HCF of 12?
A single number like 12 does not have an HCF by itself; the HCF is defined for two or more numbers.
HCF needs at least two numbers to compare. If you’re curious about 12’s factors, they’re 1, 2, 3, 4, 6, and 12. But if you pair it with another number—say 18—the common factors are 1, 2, 3, and 6. So the HCF is 6. Always remember: HCF is a team sport.
What is the HCF of 1620?
The HCF of a single number like 1620 is undefined; the concept applies only when comparing two or more numbers.
If you’re curious about 1620’s prime factors, they’re 2² × 3⁴ × 5. Those factors come in handy when you’re calculating HCF or LCM with other numbers. For example, the HCF of 1620 and 255 is 15—because 15 is the largest number that divides both.
What is the HCF of 196 and 38220?
The HCF of 196 and 38220 is 196.
Here’s a quick one: 196 divides 38220 perfectly (38220 ÷ 196 = 195). So the HCF is 196. Prime factors back this up: 196 = 2² × 7² and 38220 = 2² × 3 × 5 × 7² × 13. The overlap? 2² × 7² = 196. That means 196 is the biggest number that divides both without leaving a trace.
What is the HCF of 4052 and 12576?
The HCF of 4052 and 12576 is 4.
Euclid’s algorithm marches on: 12576 ÷ 4052 = 3 remainder 420. Then 4052 ÷ 420 = 9 remainder 272. Next, 420 ÷ 272 = 1 remainder 148. Then 272 ÷ 148 = 1 remainder 124. Next, 148 ÷ 124 = 1 remainder 24. Then 124 ÷ 24 = 5 remainder 4. Finally, 24 ÷ 4 = 6 remainder 0. The last non-zero remainder is 4, so the HCF is 4. That’s the biggest number that divides both 4052 and 12576 exactly.
What is the HCF of 1620 1725 and 255?
The HCF of 1620, 1725, and 255 is 15.
Let’s break it down. First, find the HCF of 255 and 1620. 1620 ÷ 255 = 6 remainder 90. Then 255 ÷ 90 = 2 remainder 75. Next, 90 ÷ 75 = 1 remainder 15. Finally, 75 ÷ 15 = 5 remainder 0. So HCF(255, 1620) = 15. Now check 15 against 1725: 1725 ÷ 15 = 115 with zero remainder. The HCF stays 15. That’s the largest number that divides all three evenly.
