Highest Common Factor of 456, 740, 650 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 456, 740, 650 i.e. 2 the largest integer that leaves a remainder zero for all numbers.
HCF of 456, 740, 650 is 2 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 456, 740, 650 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 456, 740, 650 is 2.
HCF(456, 740, 650) = 2
HCF of 456, 740, 650 using Euclid's algorithm
Highest common factor or Highest common divisor (hcd) can be calculated by Euclid's algotithm.
Highest common factor (HCF) of 456, 740, 650 is 2.
Highest Common Factor of 456,740,650 is 2
Step 1: Since 740 > 456, we apply the division lemma to 740 and 456, to get
740 = 456 x 1 + 284
Step 2: Since the reminder 456 ≠ 0, we apply division lemma to 284 and 456, to get
456 = 284 x 1 + 172
Step 3: We consider the new divisor 284 and the new remainder 172, and apply the division lemma to get
284 = 172 x 1 + 112
We consider the new divisor 172 and the new remainder 112,and apply the division lemma to get
172 = 112 x 1 + 60
We consider the new divisor 112 and the new remainder 60,and apply the division lemma to get
112 = 60 x 1 + 52
We consider the new divisor 60 and the new remainder 52,and apply the division lemma to get
60 = 52 x 1 + 8
We consider the new divisor 52 and the new remainder 8,and apply the division lemma to get
52 = 8 x 6 + 4
We consider the new divisor 8 and the new remainder 4,and apply the division lemma to get
8 = 4 x 2 + 0
The remainder has now become zero, so our procedure stops. Since the divisor at this stage is 4, the HCF of 456 and 740 is 4
Notice that 4 = HCF(8,4) = HCF(52,8) = HCF(60,52) = HCF(112,60) = HCF(172,112) = HCF(284,172) = HCF(456,284) = HCF(740,456) .
We can take hcf of as 1st numbers and next number as another number to apply in Euclidean lemma
Step 1: Since 650 > 4, we apply the division lemma to 650 and 4, to get
650 = 4 x 162 + 2
Step 2: Since the reminder 4 ≠ 0, we apply division lemma to 2 and 4, to get
4 = 2 x 2 + 0
The remainder has now become zero, so our procedure stops. Since the divisor at this stage is 2, the HCF of 4 and 650 is 2
Notice that 2 = HCF(4,2) = HCF(650,4) .
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Frequently Asked Questions on HCF of 456, 740, 650 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 456, 740, 650?
Answer: HCF of 456, 740, 650 is 2 the largest number that divides all the numbers leaving a remainder zero.
3. How to find HCF of 456, 740, 650 using Euclid's Algorithm?
Answer: For arbitrary numbers 456, 740, 650 apply Euclid’s Division Lemma in succession until you obtain a remainder zero. HCF is the remainder in the last but one step.