Highest Common Factor of 742, 1275 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 742, 1275 i.e. 1 the largest integer that leaves a remainder zero for all numbers.
HCF of 742, 1275 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 742, 1275 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 742, 1275 is 1.
HCF(742, 1275) = 1
HCF of 742, 1275 using Euclid's algorithm
Highest common factor or Highest common divisor (hcd) can be calculated by Euclid's algotithm.
Highest common factor (HCF) of 742, 1275 is 1.
Highest Common Factor of 742,1275 is 1
Step 1: Since 1275 > 742, we apply the division lemma to 1275 and 742, to get
1275 = 742 x 1 + 533
Step 2: Since the reminder 742 ≠ 0, we apply division lemma to 533 and 742, to get
742 = 533 x 1 + 209
Step 3: We consider the new divisor 533 and the new remainder 209, and apply the division lemma to get
533 = 209 x 2 + 115
We consider the new divisor 209 and the new remainder 115,and apply the division lemma to get
209 = 115 x 1 + 94
We consider the new divisor 115 and the new remainder 94,and apply the division lemma to get
115 = 94 x 1 + 21
We consider the new divisor 94 and the new remainder 21,and apply the division lemma to get
94 = 21 x 4 + 10
We consider the new divisor 21 and the new remainder 10,and apply the division lemma to get
21 = 10 x 2 + 1
We consider the new divisor 10 and the new remainder 1,and apply the division lemma to get
10 = 1 x 10 + 0
The remainder has now become zero, so our procedure stops. Since the divisor at this stage is 1, the HCF of 742 and 1275 is 1
Notice that 1 = HCF(10,1) = HCF(21,10) = HCF(94,21) = HCF(115,94) = HCF(209,115) = HCF(533,209) = HCF(742,533) = HCF(1275,742) .
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Frequently Asked Questions on HCF of 742, 1275 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 742, 1275?
Answer: HCF of 742, 1275 is 1 the largest number that divides all the numbers leaving a remainder zero.
3. How to find HCF of 742, 1275 using Euclid's Algorithm?
Answer: For arbitrary numbers 742, 1275 apply Euclid’s Division Lemma in succession until you obtain a remainder zero. HCF is the remainder in the last but one step.