Highest Common Factor of 650, 21138 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 650, 21138 i.e. 26 the largest integer that leaves a remainder zero for all numbers.
HCF of 650, 21138 is 26 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 650, 21138 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 650, 21138 is 26.
HCF(650, 21138) = 26
HCF of 650, 21138 using Euclid's algorithm
Highest common factor or Highest common divisor (hcd) can be calculated by Euclid's algotithm.
Highest common factor (HCF) of 650, 21138 is 26.
Highest Common Factor of 650,21138 is 26
Step 1: Since 21138 > 650, we apply the division lemma to 21138 and 650, to get
21138 = 650 x 32 + 338
Step 2: Since the reminder 650 ≠ 0, we apply division lemma to 338 and 650, to get
650 = 338 x 1 + 312
Step 3: We consider the new divisor 338 and the new remainder 312, and apply the division lemma to get
338 = 312 x 1 + 26
We consider the new divisor 312 and the new remainder 26, and apply the division lemma to get
312 = 26 x 12 + 0
The remainder has now become zero, so our procedure stops. Since the divisor at this stage is 26, the HCF of 650 and 21138 is 26
Notice that 26 = HCF(312,26) = HCF(338,312) = HCF(650,338) = HCF(21138,650) .
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Frequently Asked Questions on HCF of 650, 21138 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 650, 21138?
Answer: HCF of 650, 21138 is 26 the largest number that divides all the numbers leaving a remainder zero.
3. How to find HCF of 650, 21138 using Euclid's Algorithm?
Answer: For arbitrary numbers 650, 21138 apply Euclid’s Division Lemma in succession until you obtain a remainder zero. HCF is the remainder in the last but one step.