Question

the HCF of the following.
(i) 60, 84, 108 and 132
(ii) 84, 56, 35 and 112
Find the greatest number that will divide 58 and 145 exactly.
Find the largest number that will divide 540, 315 and 360 exactly
What is the largest number that has the multiples 168 and 288?
onsrin 9a​

Answer 1

Answer:

i)60 = (2² × 3 × 5)

84 = (2² × 3 × 7)

108 = (2² × 3³)

HCF(60,84,108) = (2² × 3) = 12

ii) 84=2x2x3x7

56=2x2x2x7

35=3x7

112=2x2x2x2x7

Therefore, HCF of 84, 56, 35 and 112 = 7

Factors for 58: 1, 2, 29, and 58

Factors for 145: 1, 5, 29, and 145

As you can see when you list out the factors of each number, 29 is the greatest number that can divide 58 and 145

540=2×2×3×3×3×5

315=3×3×5×7315=3×3×5×7

360=2×2×2×3×3×5

H.C.F=3×3×5=45

 45 is the greatest number that will divide 540, 315 and 360 exactly

Find the prime factorization of 168

168 = 2 × 2 × 2 × 3 × 7

Find the prime factorization of 288

288 = 2 × 2 × 2 × 2 × 2 × 3 × 3

To find the GCF, multiply all the prime factors common to both numbers:

Therefore, GCF = 2 × 2 × 2 × 3

GCF = 24