Highest Common Factor of 64, 88, 25, 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 64, 88, 25, 21 i.e. 1 the largest integer that leaves a remainder zero for all numbers.
HCF of 64, 88, 25, 21 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 64, 88, 25, 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 64, 88, 25, 21 is 1.
HCF(64, 88, 25, 21) = 1
HCF of 64, 88, 25, 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 64, 88, 25, 21 is 1.
Highest Common Factor of 64,88,25,21 is 1
Step 1: Since 88 > 64, we apply the division lemma to 88 and 64, to get
88 = 64 x 1 + 24
Step 2: Since the reminder 64 ≠ 0, we apply division lemma to 24 and 64, to get
64 = 24 x 2 + 16
Step 3: We consider the new divisor 24 and the new remainder 16, and apply the division lemma to get
24 = 16 x 1 + 8
We consider the new divisor 16 and the new remainder 8, and apply the division lemma to get
16 = 8 x 2 + 0
The remainder has now become zero, so our procedure stops. Since the divisor at this stage is 8, the HCF of 64 and 88 is 8
Notice that 8 = HCF(16,8) = HCF(24,16) = HCF(64,24) = HCF(88,64) .
We can take hcf of as 1st numbers and next number as another number to apply in Euclidean lemma
Step 1: Since 25 > 8, we apply the division lemma to 25 and 8, to get
25 = 8 x 3 + 1
Step 2: Since the reminder 8 ≠ 0, we apply division lemma to 1 and 8, to get
8 = 1 x 8 + 0
The remainder has now become zero, so our procedure stops. Since the divisor at this stage is 1, the HCF of 8 and 25 is 1
Notice that 1 = HCF(8,1) = HCF(25,8) .
We can take hcf of as 1st numbers and next number as another number to apply in Euclidean lemma
Step 1: Since 21 > 1, we apply the division lemma to 21 and 1, to get
21 = 1 x 21 + 0
The remainder has now become zero, so our procedure stops. Since the divisor at this stage is 1, the HCF of 1 and 21 is 1
Notice that 1 = HCF(21,1) .
HCF using Euclid's Algorithm Calculation Examples
Here are some samples of HCF using Euclid's Algorithm calculations.
Frequently Asked Questions on HCF of 64, 88, 25, 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 64, 88, 25, 21?
Answer: HCF of 64, 88, 25, 21 is 1 the largest number that divides all the numbers leaving a remainder zero.
3. How to find HCF of 64, 88, 25, 21 using Euclid's Algorithm?
Answer: For arbitrary numbers 64, 88, 25, 21 apply Euclid’s Division Lemma in succession until you obtain a remainder zero. HCF is the remainder in the last but one step.