Highest Common Factor of 40, 68, 44, 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 40, 68, 44, 102 i.e. 2 the largest integer that leaves a remainder zero for all numbers.
HCF of 40, 68, 44, 102 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 40, 68, 44, 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 40, 68, 44, 102 is 2.
HCF(40, 68, 44, 102) = 2
HCF of 40, 68, 44, 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 40, 68, 44, 102 is 2.
Highest Common Factor of 40,68,44,102 is 2
Step 1: Since 68 > 40, we apply the division lemma to 68 and 40, to get
68 = 40 x 1 + 28
Step 2: Since the reminder 40 ≠ 0, we apply division lemma to 28 and 40, to get
40 = 28 x 1 + 12
Step 3: We consider the new divisor 28 and the new remainder 12, and apply the division lemma to get
28 = 12 x 2 + 4
We consider the new divisor 12 and the new remainder 4, and apply the division lemma to get
12 = 4 x 3 + 0
The remainder has now become zero, so our procedure stops. Since the divisor at this stage is 4, the HCF of 40 and 68 is 4
Notice that 4 = HCF(12,4) = HCF(28,12) = HCF(40,28) = HCF(68,40) .
We can take hcf of as 1st numbers and next number as another number to apply in Euclidean lemma
Step 1: Since 44 > 4, we apply the division lemma to 44 and 4, to get
44 = 4 x 11 + 0
The remainder has now become zero, so our procedure stops. Since the divisor at this stage is 4, the HCF of 4 and 44 is 4
Notice that 4 = HCF(44,4) .
We can take hcf of as 1st numbers and next number as another number to apply in Euclidean lemma
Step 1: Since 102 > 4, we apply the division lemma to 102 and 4, to get
102 = 4 x 25 + 2
Step 2: Since the reminder 4 ≠ 0, we apply division lemma to 2 and 4, to get
4 = 2 x 2 + 0
The remainder has now become zero, so our procedure stops. Since the divisor at this stage is 2, the HCF of 4 and 102 is 2
Notice that 2 = HCF(4,2) = HCF(102,4) .
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Frequently Asked Questions on HCF of 40, 68, 44, 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 40, 68, 44, 102?
Answer: HCF of 40, 68, 44, 102 is 2 the largest number that divides all the numbers leaving a remainder zero.
3. How to find HCF of 40, 68, 44, 102 using Euclid's Algorithm?
Answer: For arbitrary numbers 40, 68, 44, 102 apply Euclid’s Division Lemma in succession until you obtain a remainder zero. HCF is the remainder in the last but one step.