Highest Common Factor of 32, 87, 68, 102 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 32, 87, 68, 102 i.e. 1 the largest integer that leaves a remainder zero for all numbers.
HCF of 32, 87, 68, 102 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 32, 87, 68, 102 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 32, 87, 68, 102 is 1.
HCF(32, 87, 68, 102) = 1
HCF of 32, 87, 68, 102 using Euclid's algorithm
Highest common factor or Highest common divisor (hcd) can be calculated by Euclid's algotithm.
Highest common factor (HCF) of 32, 87, 68, 102 is 1.
Highest Common Factor of 32,87,68,102 is 1
Step 1: Since 87 > 32, we apply the division lemma to 87 and 32, to get
87 = 32 x 2 + 23
Step 2: Since the reminder 32 ≠ 0, we apply division lemma to 23 and 32, to get
32 = 23 x 1 + 9
Step 3: We consider the new divisor 23 and the new remainder 9, and apply the division lemma to get
23 = 9 x 2 + 5
We consider the new divisor 9 and the new remainder 5,and apply the division lemma to get
9 = 5 x 1 + 4
We consider the new divisor 5 and the new remainder 4,and apply the division lemma to get
5 = 4 x 1 + 1
We consider the new divisor 4 and the new remainder 1,and apply the division lemma to get
4 = 1 x 4 + 0
The remainder has now become zero, so our procedure stops. Since the divisor at this stage is 1, the HCF of 32 and 87 is 1
Notice that 1 = HCF(4,1) = HCF(5,4) = HCF(9,5) = HCF(23,9) = HCF(32,23) = HCF(87,32) .
We can take hcf of as 1st numbers and next number as another number to apply in Euclidean lemma
Step 1: Since 68 > 1, we apply the division lemma to 68 and 1, to get
68 = 1 x 68 + 0
The remainder has now become zero, so our procedure stops. Since the divisor at this stage is 1, the HCF of 1 and 68 is 1
Notice that 1 = HCF(68,1) .
We can take hcf of as 1st numbers and next number as another number to apply in Euclidean lemma
Step 1: Since 102 > 1, we apply the division lemma to 102 and 1, to get
102 = 1 x 102 + 0
The remainder has now become zero, so our procedure stops. Since the divisor at this stage is 1, the HCF of 1 and 102 is 1
Notice that 1 = HCF(102,1) .
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Frequently Asked Questions on HCF of 32, 87, 68, 102 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 32, 87, 68, 102?
Answer: HCF of 32, 87, 68, 102 is 1 the largest number that divides all the numbers leaving a remainder zero.
3. How to find HCF of 32, 87, 68, 102 using Euclid's Algorithm?
Answer: For arbitrary numbers 32, 87, 68, 102 apply Euclid’s Division Lemma in succession until you obtain a remainder zero. HCF is the remainder in the last but one step.