Highest Common Factor of 3145, 3506 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 3145, 3506 i.e. 1 the largest integer that leaves a remainder zero for all numbers.
HCF of 3145, 3506 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 3145, 3506 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 3145, 3506 is 1.
HCF(3145, 3506) = 1
HCF of 3145, 3506 using Euclid's algorithm
Highest common factor or Highest common divisor (hcd) can be calculated by Euclid's algotithm.
Highest common factor (HCF) of 3145, 3506 is 1.
Highest Common Factor of 3145,3506 is 1
Step 1: Since 3506 > 3145, we apply the division lemma to 3506 and 3145, to get
3506 = 3145 x 1 + 361
Step 2: Since the reminder 3145 ≠ 0, we apply division lemma to 361 and 3145, to get
3145 = 361 x 8 + 257
Step 3: We consider the new divisor 361 and the new remainder 257, and apply the division lemma to get
361 = 257 x 1 + 104
We consider the new divisor 257 and the new remainder 104,and apply the division lemma to get
257 = 104 x 2 + 49
We consider the new divisor 104 and the new remainder 49,and apply the division lemma to get
104 = 49 x 2 + 6
We consider the new divisor 49 and the new remainder 6,and apply the division lemma to get
49 = 6 x 8 + 1
We consider the new divisor 6 and the new remainder 1,and apply the division lemma to get
6 = 1 x 6 + 0
The remainder has now become zero, so our procedure stops. Since the divisor at this stage is 1, the HCF of 3145 and 3506 is 1
Notice that 1 = HCF(6,1) = HCF(49,6) = HCF(104,49) = HCF(257,104) = HCF(361,257) = HCF(3145,361) = HCF(3506,3145) .
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Frequently Asked Questions on HCF of 3145, 3506 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 3145, 3506?
Answer: HCF of 3145, 3506 is 1 the largest number that divides all the numbers leaving a remainder zero.
3. How to find HCF of 3145, 3506 using Euclid's Algorithm?
Answer: For arbitrary numbers 3145, 3506 apply Euclid’s Division Lemma in succession until you obtain a remainder zero. HCF is the remainder in the last but one step.