Highest Common Factor of 746, 288, 741, 308 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 746, 288, 741, 308 i.e. 1 the largest integer that leaves a remainder zero for all numbers.
HCF of 746, 288, 741, 308 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 746, 288, 741, 308 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 746, 288, 741, 308 is 1.
HCF(746, 288, 741, 308) = 1
HCF of 746, 288, 741, 308 using Euclid's algorithm
Highest common factor or Highest common divisor (hcd) can be calculated by Euclid's algotithm.
Highest common factor (HCF) of 746, 288, 741, 308 is 1.
Highest Common Factor of 746,288,741,308 is 1
Step 1: Since 746 > 288, we apply the division lemma to 746 and 288, to get
746 = 288 x 2 + 170
Step 2: Since the reminder 288 ≠ 0, we apply division lemma to 170 and 288, to get
288 = 170 x 1 + 118
Step 3: We consider the new divisor 170 and the new remainder 118, and apply the division lemma to get
170 = 118 x 1 + 52
We consider the new divisor 118 and the new remainder 52,and apply the division lemma to get
118 = 52 x 2 + 14
We consider the new divisor 52 and the new remainder 14,and apply the division lemma to get
52 = 14 x 3 + 10
We consider the new divisor 14 and the new remainder 10,and apply the division lemma to get
14 = 10 x 1 + 4
We consider the new divisor 10 and the new remainder 4,and apply the division lemma to get
10 = 4 x 2 + 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 746 and 288 is 2
Notice that 2 = HCF(4,2) = HCF(10,4) = HCF(14,10) = HCF(52,14) = HCF(118,52) = HCF(170,118) = HCF(288,170) = HCF(746,288) .
We can take hcf of as 1st numbers and next number as another number to apply in Euclidean lemma
Step 1: Since 741 > 2, we apply the division lemma to 741 and 2, to get
741 = 2 x 370 + 1
Step 2: Since the reminder 2 ≠ 0, we apply division lemma to 1 and 2, 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 2 and 741 is 1
Notice that 1 = HCF(2,1) = HCF(741,2) .
We can take hcf of as 1st numbers and next number as another number to apply in Euclidean lemma
Step 1: Since 308 > 1, we apply the division lemma to 308 and 1, to get
308 = 1 x 308 + 0
The remainder has now become zero, so our procedure stops. Since the divisor at this stage is 1, the HCF of 1 and 308 is 1
Notice that 1 = HCF(308,1) .
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Frequently Asked Questions on HCF of 746, 288, 741, 308 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 746, 288, 741, 308?
Answer: HCF of 746, 288, 741, 308 is 1 the largest number that divides all the numbers leaving a remainder zero.
3. How to find HCF of 746, 288, 741, 308 using Euclid's Algorithm?
Answer: For arbitrary numbers 746, 288, 741, 308 apply Euclid’s Division Lemma in succession until you obtain a remainder zero. HCF is the remainder in the last but one step.