The highest common factor (HCF) of 69 is 69. Every number is a factor of itself, so 69’s HCF is the number itself, with factors 1, 3, 23, and 69.
What are the factors of 69?
The factors of 69 are 1, 3, 23, and 69.
Sixty-nine is the product of two primes (3 × 23), so its factors pair up neatly. Try dividing 69 by every integer from 1 to 69—only 1, 3, 23, and 69 divide without a remainder. Math is Fun has a great visual guide if you’d rather draw factor trees than do long division.
What is the greatest common factor of 69?
The greatest common factor (GCF) of 69 is 69.
When you’re dealing with a single number, the GCF is always the number itself. (Every integer is divisible by itself, after all.) If you were comparing 69 to another number, you’d list both sets of factors and pick the largest one they share—try that trick next time you’re simplifying fractions.
What is the GCF of 69 and 75?
The GCF of 69 and 75 is 3.
Both numbers are odd, but only 3 divides both evenly. List their factors: 69 has 1, 3, 23, 69, while 75 has 1, 3, 5, 15, 25, 75. The biggest overlap is 3. Quick check: 69 ÷ 3 = 23 and 75 ÷ 3 = 25, so the division works cleanly.
What’s the GCF of 69 and 84?
The GCF of 69 and 84 is 3.
Start by listing 84’s factors: 1, 2, 3, 4, 6, 7, 12, 14, 21, 28, 42, 84. Compare that to 69’s factors (1, 3, 23, 69). Only 1 and 3 appear in both lists, so 3 is the GCF. Prefer a shortcut? Use the Euclidean algorithm: 84 ÷ 69 = 1 remainder 15, then 69 ÷ 15 = 4 remainder 9, then 15 ÷ 9 = 1 remainder 6, then 9 ÷ 6 = 1 remainder 3, finally 6 ÷ 3 = 2 remainder 0—so 3 is the GCF.
What is the HCF of 63, 70 and 77?
The HCF of 63, 70, and 77 is 7.
Break each number down to primes: 63 = 3² × 7, 70 = 2 × 5 × 7, 77 = 7 × 11. The only prime they share is 7. You could also list the factors: 63 (1, 3, 7, 9, 21, 63), 70 (1, 2, 5, 7, 10, 14, 35, 70), 77 (1, 7, 11, 77). The largest number common to all three lists is 7.
What is the GCF of 60?
For any single number, the greatest common factor is the number itself. (Every integer is divisible by itself.) If you were comparing 60 to another number, you’d list both sets of factors and pick the largest overlap. For example, the GCF of 60 and 30 is 30.
What is a square root of 69?
The square root of 69 is approximately 8.3066.
Pull out a calculator or square-root table for a precise value, since 69 isn’t a perfect square. Rounded to two decimals, √69 ≈ 8.31. The closest perfect squares are 64 (8²) and 81 (9²), so √69 falls right in between. Trying to estimate by hand? 8.3² = 68.89—just a hair below 69.
What are the first 10 multiples of 69?
The first 10 multiples of 69 are 69, 138, 207, 276, 345, 414, 483, 552, 621, and 690.
Multiply 69 by 1 through 10 to generate the sequence. Each step adds another 69, so the list grows in a straight line. Add them all up and you get 3,795—handy for quick arithmetic checks or summing practice.
What is a factor of 63?
A factor of 63 is any integer that divides 63 without a remainder.
The positive factors of 63 are 1, 3, 7, 9, 21, and 63. Don’t forget the negatives: –1, –3, –7, –9, –21, –63. Prime factorization (3² × 7) explains why these numbers divide evenly. Britannica has a quick refresher on how factors work.
What is the HCF of 92 and 64?
The HCF of 92 and 64 is 4.
List 92’s factors: 1, 2, 4, 23, 46, 92. List 64’s factors: 1, 2, 4, 8, 16, 32, 64. The largest match is 4. Or use the Euclidean algorithm: 92 ÷ 64 = 1 remainder 28, 64 ÷ 28 = 2 remainder 8, 28 ÷ 8 = 3 remainder 4, 8 ÷ 4 = 2 remainder 0—so 4 is the HCF.
What is the HCF of 18 and 48?
The HCF of 18 and 48 is 6.
Eighteen’s factors: 1, 2, 3, 6, 9, 18. Forty-eight’s factors: 1, 2, 3, 4, 6, 8, 12, 16, 24, 48. The biggest overlap is 6. Prime-factor method works too: 18 = 2 × 3², 48 = 2⁴ × 3, so the HCF is 2 × 3 = 6.
What is the HCF of 825, 675 and 450?
The HCF of 825, 675, and 450 is 75.
Prime-factor each number: 825 = 3 × 5² × 11, 675 = 3³ × 5², 450 = 2 × 3² × 5². The shared primes are 3 and 5², which multiply to 3 × 25 = 75. That makes 75 the largest integer dividing all three numbers evenly.
What is the GCF of 60 and 90?
The GCF of 60 and 90 is 30.
Both numbers share the factors 1, 2, 3, 5, 6, 10, 15, and 30. The largest is 30. Prime-factor method: 60 = 2² × 3 × 5, 90 = 2 × 3² × 5, so the GCF is 2 × 3 × 5 = 30.
What is the GCF of 77 and 63?
The GCF of 77 and 63 is 7.
Prime-factor each: 77 = 7 × 11, 63 = 3² × 7. The only common prime is 7, so 7 is the GCF. Listing the factors (77: 1, 7, 11, 77; 63: 1, 3, 7, 9, 21, 63) also shows 7 as the largest overlap.
What is the HCF of 465?
When you ask for the HCF of a single number, the answer is always the number itself. (Every integer is divisible by itself.) If you were comparing 465 to another number, you’d list both sets of factors and pick the largest overlap. For example, the HCF of 465 and 930 is 465.
What is the LCM of 63, 70 and 77?
The LCM of 63, 70, and 77 is 6,930.
To find the least common multiple, multiply the highest powers of all primes present: 2¹ × 3² × 5¹ × 7¹ × 11¹ = 6,930. That’s the smallest number divisible by 63, 70, and 77 without any remainder.
What is the HCF of 825, 675 and 450?
The HCF of 825, 675, and 450 is 75.
Prime-factor each number: 825 = 3 × 5² × 11, 675 = 3³ × 5², 450 = 2 × 3² × 5². The common primes are 3 and 5², which multiply to 3 × 25 = 75. That makes 75 the largest integer dividing all three numbers evenly.
