The HCF of 16 and 21 is 1. The highest common factor of 16 and 21 is the value that divides 16 and 21 evenly. The factors of 16 and 21 are 1, 2, 4, 8, 16and 1, 3, 7 and 21, respectively. Students will learn the methods, prime factorisation, long division and listing common factors effortlessly in this article. Various HCF concepts can be well memorized by the students using the study materials available at BYJU’S.
Also read: Highest common factor
What is the HCF of 16 and 21?
The answer to this question is 1. The HCF of 16 and 21 determined using three various methods are provided in brief in this article. The HCF of 16 and 21 is 1 which divides the given two numbers evenly.
How to Find HCF of 16 and 21?
The HCF of 16 and 21 can be found using the methods below:
- Prime Factorisation
- Long Division method
- Listing common factors
HCF of 16 and 21 by Prime Factorisation Method
The prime factorisation of 16 and 21 are:
16 = 2 × 2 × 2 × 2
21 = 3 × 7
There is no common prime factor for 16 and 21.
Hence, HCF (16, 21) = 1
HCF of 16 and 21 by Long Division Method
We have to divide 16 and 21 by their prime factors so that the HCF of 16 and 21 can be found using the division method. The divisor we get with zero as the remainder is the HCF of 16 and 21.
No further division can be done.
Hence, HCF (16, 21) = 1
HCF of 16 and 21 by Listing Common Factors
The HCF of 16 and 21 can be determined by listing the common factors as given below:
Factors of 16: 1, 2, 4, 8, 16
Factors of 21: 1, 3, 7, 21
There is one common factor of 16 and 21, and that is 1.
Therefore, the highest common factor of 16 and 21 is 1.
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Video Lesson on Properties of HCF and LCM
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HCF of 16 and 21 Solved Example
Question: Find the HCF of 16 and 21 if the LCM is 336.
Solution:
Given
LCM = 336
We know that
HCF × LCM = 16 × 21
HCF = (16 × 21)/336
HCF = 1
Hence, the HCF is 1.
Frequently Asked Questions on HCF of 16 and 21
What is the HCF of 16 and 21?
Calculate the HCF of 16 and 21 using the long division method.
Write the methods used to find HCF of 16 and 21.
If LCM = 336 and HCF = 1 for two numbers, find the other number when one number is 16.
Consider y as the other number
Given LCM = 336 and HCF = 1
HCF × LCM = 16 × y
y = (HCF × LCM)/16
y = (1 × 336)/16
y = 21
Therefore, the other number is 21.
Show the relation between HCF and LCM of 16 and 21.
The relation between HCF and LCM of 16 and 21 is
HCF × LCM = 16 × 21
HCF × LCM = 336
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