Highest Common Factor of 78, 21, 15, 32 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 78, 21, 15, 32 i.e. 1 the largest integer that leaves a remainder zero for all numbers.
HCF of 78, 21, 15, 32 is 1 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 78, 21, 15, 32 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 78, 21, 15, 32 is 1.
HCF(78, 21, 15, 32) = 1
HCF of 78, 21, 15, 32 using Euclid's algorithm
Highest common factor or Highest common divisor (hcd) can be calculated by Euclid's algotithm.
Highest common factor (HCF) of 78, 21, 15, 32 is 1.
Highest Common Factor of 78,21,15,32 is 1
Step 1: Since 78 > 21, we apply the division lemma to 78 and 21, to get
78 = 21 x 3 + 15
Step 2: Since the reminder 21 ≠ 0, we apply division lemma to 15 and 21, to get
21 = 15 x 1 + 6
Step 3: We consider the new divisor 15 and the new remainder 6, and apply the division lemma to get
15 = 6 x 2 + 3
We consider the new divisor 6 and the new remainder 3, and apply the division lemma to get
6 = 3 x 2 + 0
The remainder has now become zero, so our procedure stops. Since the divisor at this stage is 3, the HCF of 78 and 21 is 3
Notice that 3 = HCF(6,3) = HCF(15,6) = HCF(21,15) = HCF(78,21) .
We can take hcf of as 1st numbers and next number as another number to apply in Euclidean lemma
Step 1: Since 15 > 3, we apply the division lemma to 15 and 3, to get
15 = 3 x 5 + 0
The remainder has now become zero, so our procedure stops. Since the divisor at this stage is 3, the HCF of 3 and 15 is 3
Notice that 3 = HCF(15,3) .
We can take hcf of as 1st numbers and next number as another number to apply in Euclidean lemma
Step 1: Since 32 > 3, we apply the division lemma to 32 and 3, to get
32 = 3 x 10 + 2
Step 2: Since the reminder 3 ≠ 0, we apply division lemma to 2 and 3, to get
3 = 2 x 1 + 1
Step 3: We consider the new divisor 2 and the new remainder 1, and apply the division lemma to get
2 = 1 x 2 + 0
The remainder has now become zero, so our procedure stops. Since the divisor at this stage is 1, the HCF of 3 and 32 is 1
Notice that 1 = HCF(2,1) = HCF(3,2) = HCF(32,3) .
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Frequently Asked Questions on HCF of 78, 21, 15, 32 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 78, 21, 15, 32?
Answer: HCF of 78, 21, 15, 32 is 1 the largest number that divides all the numbers leaving a remainder zero.
3. How to find HCF of 78, 21, 15, 32 using Euclid's Algorithm?
Answer: For arbitrary numbers 78, 21, 15, 32 apply Euclid’s Division Lemma in succession until you obtain a remainder zero. HCF is the remainder in the last but one step.