Highest Common Factor of 748, 202, 64 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 748, 202, 64 i.e. 2 the largest integer that leaves a remainder zero for all numbers.
HCF of 748, 202, 64 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 748, 202, 64 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 748, 202, 64 is 2.
HCF(748, 202, 64) = 2
HCF of 748, 202, 64 using Euclid's algorithm
Highest common factor or Highest common divisor (hcd) can be calculated by Euclid's algotithm.
Highest common factor (HCF) of 748, 202, 64 is 2.
Highest Common Factor of 748,202,64 is 2
Step 1: Since 748 > 202, we apply the division lemma to 748 and 202, to get
748 = 202 x 3 + 142
Step 2: Since the reminder 202 ≠ 0, we apply division lemma to 142 and 202, to get
202 = 142 x 1 + 60
Step 3: We consider the new divisor 142 and the new remainder 60, and apply the division lemma to get
142 = 60 x 2 + 22
We consider the new divisor 60 and the new remainder 22,and apply the division lemma to get
60 = 22 x 2 + 16
We consider the new divisor 22 and the new remainder 16,and apply the division lemma to get
22 = 16 x 1 + 6
We consider the new divisor 16 and the new remainder 6,and apply the division lemma to get
16 = 6 x 2 + 4
We consider the new divisor 6 and the new remainder 4,and apply the division lemma to get
6 = 4 x 1 + 2
We consider the new divisor 4 and the new remainder 2,and apply the division lemma 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 748 and 202 is 2
Notice that 2 = HCF(4,2) = HCF(6,4) = HCF(16,6) = HCF(22,16) = HCF(60,22) = HCF(142,60) = HCF(202,142) = HCF(748,202) .
We can take hcf of as 1st numbers and next number as another number to apply in Euclidean lemma
Step 1: Since 64 > 2, we apply the division lemma to 64 and 2, to get
64 = 2 x 32 + 0
The remainder has now become zero, so our procedure stops. Since the divisor at this stage is 2, the HCF of 2 and 64 is 2
Notice that 2 = HCF(64,2) .
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Frequently Asked Questions on HCF of 748, 202, 64 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 748, 202, 64?
Answer: HCF of 748, 202, 64 is 2 the largest number that divides all the numbers leaving a remainder zero.
3. How to find HCF of 748, 202, 64 using Euclid's Algorithm?
Answer: For arbitrary numbers 748, 202, 64 apply Euclid’s Division Lemma in succession until you obtain a remainder zero. HCF is the remainder in the last but one step.