Highest Common Factor of 363, 7507, 1960 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 363, 7507, 1960 i.e. 1 the largest integer that leaves a remainder zero for all numbers.
HCF of 363, 7507, 1960 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 363, 7507, 1960 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 363, 7507, 1960 is 1.
HCF(363, 7507, 1960) = 1
HCF of 363, 7507, 1960 using Euclid's algorithm
Highest common factor or Highest common divisor (hcd) can be calculated by Euclid's algotithm.
Highest common factor (HCF) of 363, 7507, 1960 is 1.
Highest Common Factor of 363,7507,1960 is 1
Step 1: Since 7507 > 363, we apply the division lemma to 7507 and 363, to get
7507 = 363 x 20 + 247
Step 2: Since the reminder 363 ≠ 0, we apply division lemma to 247 and 363, to get
363 = 247 x 1 + 116
Step 3: We consider the new divisor 247 and the new remainder 116, and apply the division lemma to get
247 = 116 x 2 + 15
We consider the new divisor 116 and the new remainder 15,and apply the division lemma to get
116 = 15 x 7 + 11
We consider the new divisor 15 and the new remainder 11,and apply the division lemma to get
15 = 11 x 1 + 4
We consider the new divisor 11 and the new remainder 4,and apply the division lemma to get
11 = 4 x 2 + 3
We consider the new divisor 4 and the new remainder 3,and apply the division lemma to get
4 = 3 x 1 + 1
We consider the new divisor 3 and the new remainder 1,and apply the division lemma to get
3 = 1 x 3 + 0
The remainder has now become zero, so our procedure stops. Since the divisor at this stage is 1, the HCF of 363 and 7507 is 1
Notice that 1 = HCF(3,1) = HCF(4,3) = HCF(11,4) = HCF(15,11) = HCF(116,15) = HCF(247,116) = HCF(363,247) = HCF(7507,363) .
We can take hcf of as 1st numbers and next number as another number to apply in Euclidean lemma
Step 1: Since 1960 > 1, we apply the division lemma to 1960 and 1, to get
1960 = 1 x 1960 + 0
The remainder has now become zero, so our procedure stops. Since the divisor at this stage is 1, the HCF of 1 and 1960 is 1
Notice that 1 = HCF(1960,1) .
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Frequently Asked Questions on HCF of 363, 7507, 1960 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 363, 7507, 1960?
Answer: HCF of 363, 7507, 1960 is 1 the largest number that divides all the numbers leaving a remainder zero.
3. How to find HCF of 363, 7507, 1960 using Euclid's Algorithm?
Answer: For arbitrary numbers 363, 7507, 1960 apply Euclid’s Division Lemma in succession until you obtain a remainder zero. HCF is the remainder in the last but one step.