Highest Common Factor of 72, 42, 20, 8 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 72, 42, 20, 8 i.e. 2 the largest integer that leaves a remainder zero for all numbers.
HCF of 72, 42, 20, 8 is 2 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 72, 42, 20, 8 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 72, 42, 20, 8 is 2.
HCF(72, 42, 20, 8) = 2
HCF of 72, 42, 20, 8 using Euclid's algorithm
Highest common factor or Highest common divisor (hcd) can be calculated by Euclid's algotithm.
Highest common factor (HCF) of 72, 42, 20, 8 is 2.
Highest Common Factor of 72,42,20,8 is 2
Step 1: Since 72 > 42, we apply the division lemma to 72 and 42, to get
72 = 42 x 1 + 30
Step 2: Since the reminder 42 ≠ 0, we apply division lemma to 30 and 42, to get
42 = 30 x 1 + 12
Step 3: We consider the new divisor 30 and the new remainder 12, and apply the division lemma to get
30 = 12 x 2 + 6
We consider the new divisor 12 and the new remainder 6, and apply the division lemma to get
12 = 6 x 2 + 0
The remainder has now become zero, so our procedure stops. Since the divisor at this stage is 6, the HCF of 72 and 42 is 6
Notice that 6 = HCF(12,6) = HCF(30,12) = HCF(42,30) = HCF(72,42) .
We can take hcf of as 1st numbers and next number as another number to apply in Euclidean lemma
Step 1: Since 20 > 6, we apply the division lemma to 20 and 6, to get
20 = 6 x 3 + 2
Step 2: Since the reminder 6 ≠ 0, we apply division lemma to 2 and 6, to get
6 = 2 x 3 + 0
The remainder has now become zero, so our procedure stops. Since the divisor at this stage is 2, the HCF of 6 and 20 is 2
Notice that 2 = HCF(6,2) = HCF(20,6) .
We can take hcf of as 1st numbers and next number as another number to apply in Euclidean lemma
Step 1: Since 8 > 2, we apply the division lemma to 8 and 2, to get
8 = 2 x 4 + 0
The remainder has now become zero, so our procedure stops. Since the divisor at this stage is 2, the HCF of 2 and 8 is 2
Notice that 2 = HCF(8,2) .
HCF using Euclid's Algorithm Calculation Examples
Here are some samples of HCF using Euclid's Algorithm calculations.
Frequently Asked Questions on HCF of 72, 42, 20, 8 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 72, 42, 20, 8?
Answer: HCF of 72, 42, 20, 8 is 2 the largest number that divides all the numbers leaving a remainder zero.
3. How to find HCF of 72, 42, 20, 8 using Euclid's Algorithm?
Answer: For arbitrary numbers 72, 42, 20, 8 apply Euclid’s Division Lemma in succession until you obtain a remainder zero. HCF is the remainder in the last but one step.