Find the HCF of the following sets.a) 144, 180b) 276,1242
c) 136, 170,255
d) 1050, 750

The listing method involves the process of listing the factors of the given numbers. Then separate all the common factors and then the greatest common factor will be the HCF of those numbers.
I) 144, 180
Answer-
All possible factors of 144 – 2, 3, 4, 6, 8, 9, 12, 16, 18, 24, 36, 48, 72, 144
All possible factors of 180 – 2, 3, 4, 5, 6, 9, 10, 12, 15,18, 20, 30, 36, 45, 60, 90, 180
Common factors are – 2, 3, 4, 6, 9, 12, 18, 36
Greatest common factor is 36, so 36 is the HCF of 144 and 180.

II) 276, 1242
Answer-
All possible factors of 276 – 2, 3, 4, 6, 12, 23, 46, 69, 92, 138, 276
All possible factors of 1242 – 2, 3, 6, 9, 12, 18, 23, 27, 46, 54, 69, 138, 207, 414, 621, 1242
Common factors are – 2, 3, 6, 12, 23, 46, 69, 138
Greatest common factor is 138, so 138 is the HCF of 276 and 1242.

IlI) 136, 170, 255
Answer-
All possible factors of 136 – 2, 4, 8, 17, 34, 68, 136
All possible factors of 170 – 2, 5, 10, 17, 34, 85, 170
All possible factors of 255 – 3, 5, 15, 17, 51, 85, 255
Common factors are – 17
Greatest common factor is 17, so 17 is the HCF of 136, 170 and 255.

lv) 136, 170, 255
Answer-
All possible factors of 1050 – 2, 3, 5, 6, 7, 10, 14, 15, 21, 25, 30, 35, 42, 50, 70, 75, 105, 150, 175, 210, 350, 525, 1050
All possible factors of 750 – 2, 3, 5, 6, 10, 15, 25, 30, 50, 75, 125, 150, 250, 375, 750
Common factors are – 2, 3, 5, 6, 10, 15, 25, 30, 50, 75, 150
Greatest common factor is 150, so 150 is the HCF of 136, 170 and 255.

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Updated on: 10-Oct-2022

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