Highest Common Factor of 60, 90, 21 using Euclid's algorithm
Created By : Jatin Gogia
Reviewed By : Rajasekhar Valipishetty
Last Updated : Apr 06, 2023
HCF Calculator using the Euclid Division Algorithm helps you to find the Highest common factor (HCF) easily for 60, 90, 21 i.e. 3 the largest integer that leaves a remainder zero for all numbers.
HCF of 60, 90, 21 is 3 the largest number which exactly divides all the numbers i.e. where the remainder is zero. Let us get into the working of this example.
Consider we have numbers 60, 90, 21 and we need to find the HCF of these numbers. To do so, we need to choose the largest integer first and then as per Euclid's Division Lemma a = bq + r where 0 ≤ r ≤ b
Highest common factor (HCF) of 60, 90, 21 is 3.
HCF(60, 90, 21) = 3
HCF of 60, 90, 21 using Euclid's algorithm
Highest common factor or Highest common divisor (hcd) can be calculated by Euclid's algotithm.
Highest common factor (HCF) of 60, 90, 21 is 3.
Highest Common Factor of 60,90,21 is 3
Step 1: Since 90 > 60, we apply the division lemma to 90 and 60, to get
90 = 60 x 1 + 30
Step 2: Since the reminder 60 ≠ 0, we apply division lemma to 30 and 60, to get
60 = 30 x 2 + 0
The remainder has now become zero, so our procedure stops. Since the divisor at this stage is 30, the HCF of 60 and 90 is 30
Notice that 30 = HCF(60,30) = HCF(90,60) .
We can take hcf of as 1st numbers and next number as another number to apply in Euclidean lemma
Step 1: Since 30 > 21, we apply the division lemma to 30 and 21, to get
30 = 21 x 1 + 9
Step 2: Since the reminder 21 ≠ 0, we apply division lemma to 9 and 21, to get
21 = 9 x 2 + 3
Step 3: We consider the new divisor 9 and the new remainder 3, and apply the division lemma to get
9 = 3 x 3 + 0
The remainder has now become zero, so our procedure stops. Since the divisor at this stage is 3, the HCF of 30 and 21 is 3
Notice that 3 = HCF(9,3) = HCF(21,9) = HCF(30,21) .
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Frequently Asked Questions on HCF of 60, 90, 21 using Euclid's Algorithm
1. What is the Euclid division algorithm?
Answer: Euclid's Division Algorithm is a technique to compute the Highest Common Factor (HCF) of given positive integers.
2. what is the HCF of 60, 90, 21?
Answer: HCF of 60, 90, 21 is 3 the largest number that divides all the numbers leaving a remainder zero.
3. How to find HCF of 60, 90, 21 using Euclid's Algorithm?
Answer: For arbitrary numbers 60, 90, 21 apply Euclid’s Division Lemma in succession until you obtain a remainder zero. HCF is the remainder in the last but one step.