What Are The Prime Factors Of 70

Factors of seventy are the list of integers that dissever seventy exactly without leaving a remainder. i, 2, 5, 7, 10, 14, 35, and seventy are the eight factors of seventy.
1 is the smallest gene while 70 itself is the biggest gene of lxx. The sum of all the factors of seventy is 144. The pair factors of 70 are a set of ii numbers that give 70 every bit a production on
multiplication
with each other. The pair factors of 70 are (one, 70), (2, 35), and (v, 14).
The prime number factorization of 70 is 2 × 5 × vii, with 2, v, and vii equally the prime factors of 70.


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NCERT Solutions for Class 6 Maths Playing With Numbers

Key Terms:
Factors of 70, Prime Factorization, Pair Factors, Balance, Multiplication, Prime Factor, Integers, Partitioning, Prime


What are Factors of 70?

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Factors of lxx are the numbers that divide 70 exactly leaving 0 as the remainder on sectionalisation. seventy is an even
composite number

which implies that it has many factors other than i and 70. Hence, in that location are eight factors of 70 which are 1, 2, 5, 7, 10, 14, 35, and lxx.

Factors of seventy:


1, 2, 5, 7, 10, 14, 35, seventy


Factors of 70

Factors of 70


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Factors of 70 in Pair

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Factors of 70 in pairs are the 2 numbers that when multiplied together give the value of 70. The pair factors of lxx tin be positive every bit well as negative, It is and so because the negative pair cistron would eventually event in the positive value of 70 only on multiplication with each other.

Positive Pair Factors of 70

The positive pair factors of 70 are (1, 70), (2, 35), and (5, 14).

Positive Factors of 70 Positive Pair Factors of lxx
1 × lxx (1, 70)
2 × 35 (two, 35)
5 × 14 (5, fourteen)
seven × ten (vii, 10)

Negative Pair Factors of 70

The negative pair factors of 70 are (-1, -seventy), (-2, -35), and (-5, -14).

Negative Factors of 70 Negative Pair Factors of lxx
-1 × -70 (-1, -70)
-2 × -35 (-2, -35)
-5 × -14 (-5, -14)
-vii × -10 (-seven, -ten)

How to Calculate Factors of 70?

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Factors of a number tin can be calculated through various methods of which the simplest 1 is the
division
method. The steps to calculate the factors of 70 through the sectionalization method are as follows:

  • Step 1:
    Write downwards the two smallest factors of lxx apart from 1. Consider the two smallest factors of 70 which are 2 and five.
  • Footstep 2:
    Now, divide seventy by 2 and 5.

seventy / 2 = 35

70 / 5 = 14

Thus, 2, 5, xiv, and 35 are the factors of 70.

  • Pace 3:
    Now, proceed with the next factor of 70 which is 7. Divide the number lxx past 7.

70 / 7 = x

Thus, 2, 5, 7, 10, 14, and 35 are the factors of seventy.

  • Step 4:
    At last, include 1 and the number itself to the factors.

Therefore, the factors of lxx are calculated as 1, 2, 5, vii, ten, 14, 35, and seventy.


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Greatest Common Divisor


Factors of lxx by Prime Factorization

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seventy is a composite number which means that it should take prime factors. Here is a step-by-step procedure to calculate the prime number factors of 70:

Footstep 1:
Separate 70 with the smallest prime factor 2.

70 ÷ 2 = 35

Step 2:
Now, divide 45 by ii and 3, still, we will get a fractional value, thus, we need to proceed with the next
prime number number
say 5.

35 ÷ 5 = 7

Pace 3:
If we divide seven by 5, w will get a
fraction. Motility on with the next prime factor, vii.

7 ÷ 7 = 1

We have received 1 at the end of the sectionalization process, which ways we cannot proceed further.
The

prime factorization

of 70 is thus written every bit two × 5 × 7.

Prime Factorization of 70

Prime Factorization of lxx


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Prime number Formula

Factor Tree of 70

Factors of 70 tin be represented with the assist of the factor tree also. The cistron tree of 70 is as follows:

Factor Tree of 70

Cistron Tree of 70


Solved Examples on Factors of seventy

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Instance 1: What are the common factors of lxx and 71?

Solution:
The factors of 70 and 71 are as follows:

  • Factors of 70:
    1, 2, 5, 7, 10, xiv, 35, and 70.
  • Factors of 71:
    1 and 71.

71 is a prime number which means the only mutual factor of 70 and 71 is 1.

Example ii: What are the common factors of seventy and 35?

Solution:
seventy is twice the number 35. The factors of seventy and 35 are

  • Factors of lxx:
    1, ii, 5, seven, 10, fourteen, 35, and 70.
  • Factors of 35:
    i, 5, 7, and 35.

Hence, the common factors of lxx and 35 are four in number which are 1, 5, seven, and 35.


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Things to Remember

  • Factors of seventy are those numbers that split up 70 exactly leaving no remainder.
  • Factors of 70 are one, two, 5, 7, 10, 14, 35, and 70.
  • The prime factorization of seventy is expressed every bit 2 x 5 ten 7.
  • 2, 5, and seven are the three prime factors of the number 70.
  • The sum of all the factors of lxx is 144.
  • We tin calculate the factors of 70 past the division method and prime factorization.

Sample Questions

Ques. What are the mutual factors of 70 and 69?
(2 Marks)

Ans.
The factors of 70 and 69 are:

  • Factors of 70 are one, two, 5, 7, ten, fourteen, 35, and lxx.
  • Factors of 69 are ane, 3, 23, and 69.

Thus, there is merely one common factor of 70 and 69 which is 1.

Ques. Sunneeta wants to empty two buckets full of water with a capacity of 140 liters and lxx liters respectively. She has to empty the buckets with the help of a glass. Find out the capacity of the glass she should choose and so that no h2o remains in whatsoever of the buckets.
(3 Marks)

Ans.
It is given that,

  • Capacity of Offset Bucket = 140 liters
    Chapters of Second Bucket = seventy liters

In guild to find the capacity of the drinking glass, we need to summate the HCF (Highest Mutual Cistron) of seventy and 140.

  • lxx = 1 × 2 × v × vii
  • 140 = 1 × two × 2 × 5 × 7

Thus, the HCF of 70 and 140 = two × 5 × 7 = 70.
Therefore, Suneeta volition use a glass with a capacity of seventy liters.

Ques. What are the common factors of lxx, 420, and 560?
(3 Marks)

Ans.
The factors of 70, 420, and 560 are:

  • Factors of 70:
    1, 2, 5, 7, 10, xiv, 35, seventy
  • Factors of 420:
    1, 2, 3, 4, 5, half-dozen, 7, 10, 12, 14, xv, twenty, 21, 28, 30, 35, 42, 60, 70, 84, 105, 140, 210, 420
  • Factors of 560:
    i, 2, 4, v, seven, 8, 10, fourteen, xvi, xx, 28, 35, 40, 56, seventy, 80, 112, 140, 280, 560

Thus, the common factors of 70, 420, and 560 are 1, 2, v, 7, 10, 35, and 70.

Ques. What number must be added to 6 so that it becomes a factor of 70? What all numbers can she add?
(3 Marks)

Ans.
Allow usa consider that she ten to vi.
Thus, (10 + half-dozen) is a factor of 70.

Factors of 70 greater than half-dozen: vii, 10, 14, 35, 70

  • 10 + vi = 7
  • x + vi = 10
  • x + half dozen = fourteen
  • x + 6 = 35
  • x + half-dozen = 70

Thus, ane, 4, 8, 29, or 64 can exist added to half-dozen to become a factor of seventy.

Ques. Name the Greatest Mutual Factor of 70 and 47.
(2 Marks)

Ans.
We know that,

  • Factors of seventy: 1, 2, five, 7, 10, 14, 35, seventy
  • Factors of 47: i, 47.

Thus, 70 and 47 have merely one common cistron which is 1 which implies that 70 and 47 are co-prime number. The Greatest Mutual Factor (GCF) of 70 and 47 is thus 1.

Ques. List the common factors of seventy and 15.

(2 Marks)

Ans.
The factors of 70 and fifteen are

  • Factors of 70: 1, 2, 5, 7, 10, 14, 35, 70.
  • Factors of xv: one, 3, 5, fifteen.

Thus, 1, and 5 are the mutual factors of 70 and 15.

Ques. Listing the factors of 70.
(ane Mark)

Ans.
The number 70 has eight factors in total which are 1, 2, v, vii, 10, xiv, 35, and 70.

Ques. Write down the prime number factorization of lxx.
(1 Marking)

Ans.
The prime factorization of 70 is 2 × five × vii, where, 2, 5, and 7 are the prime factors of 70.

Ques. State the positive and negative pair factors of lxx.
(ii Marks)

Ans.
Given below are the positive and negative pair factors of 70:

  • Positive Pair Factors of 70: (ane, seventy), (ii, 35), (v, 14).
  • Negative Pair Factors of 70: (-1, -lxx), (-2, -35), (-five, -14).

Ques. Is 14 a factor of 70 or not?

(two Marks)

Ans.
Nosotros need to divide 70 by fourteen to bank check whether 14 is a gene of 70 or non.

On dividing seventy by 14, we get 5 and it leaves a remainder of 0.

Thus, xiv is a factor of 70.


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Source: https://collegedunia.com/exams/factors-of-70-mathematics-articleid-7399

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