Highest Common Factor of 875, 60004 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 875, 60004 i.e. 7 the largest integer that leaves a remainder zero for all numbers.
HCF of 875, 60004 is 7 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 875, 60004 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 875, 60004 is 7.
HCF(875, 60004) = 7
HCF of 875, 60004 using Euclid's algorithm
Highest common factor or Highest common divisor (hcd) can be calculated by Euclid's algotithm.
Highest common factor (HCF) of 875, 60004 is 7.
Highest Common Factor of 875,60004 is 7
Step 1: Since 60004 > 875, we apply the division lemma to 60004 and 875, to get
60004 = 875 x 68 + 504
Step 2: Since the reminder 875 ≠ 0, we apply division lemma to 504 and 875, to get
875 = 504 x 1 + 371
Step 3: We consider the new divisor 504 and the new remainder 371, and apply the division lemma to get
504 = 371 x 1 + 133
We consider the new divisor 371 and the new remainder 133,and apply the division lemma to get
371 = 133 x 2 + 105
We consider the new divisor 133 and the new remainder 105,and apply the division lemma to get
133 = 105 x 1 + 28
We consider the new divisor 105 and the new remainder 28,and apply the division lemma to get
105 = 28 x 3 + 21
We consider the new divisor 28 and the new remainder 21,and apply the division lemma to get
28 = 21 x 1 + 7
We consider the new divisor 21 and the new remainder 7,and apply the division lemma to get
21 = 7 x 3 + 0
The remainder has now become zero, so our procedure stops. Since the divisor at this stage is 7, the HCF of 875 and 60004 is 7
Notice that 7 = HCF(21,7) = HCF(28,21) = HCF(105,28) = HCF(133,105) = HCF(371,133) = HCF(504,371) = HCF(875,504) = HCF(60004,875) .
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Frequently Asked Questions on HCF of 875, 60004 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 875, 60004?
Answer: HCF of 875, 60004 is 7 the largest number that divides all the numbers leaving a remainder zero.
3. How to find HCF of 875, 60004 using Euclid's Algorithm?
Answer: For arbitrary numbers 875, 60004 apply Euclid’s Division Lemma in succession until you obtain a remainder zero. HCF is the remainder in the last but one step.