Highest Common Factor of 451, 732, 974, 406 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 451, 732, 974, 406 i.e. 1 the largest integer that leaves a remainder zero for all numbers.
HCF of 451, 732, 974, 406 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 451, 732, 974, 406 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 451, 732, 974, 406 is 1.
HCF(451, 732, 974, 406) = 1
HCF of 451, 732, 974, 406 using Euclid's algorithm
Highest common factor or Highest common divisor (hcd) can be calculated by Euclid's algotithm.
Highest common factor (HCF) of 451, 732, 974, 406 is 1.
Highest Common Factor of 451,732,974,406 is 1
Step 1: Since 732 > 451, we apply the division lemma to 732 and 451, to get
732 = 451 x 1 + 281
Step 2: Since the reminder 451 ≠ 0, we apply division lemma to 281 and 451, to get
451 = 281 x 1 + 170
Step 3: We consider the new divisor 281 and the new remainder 170, and apply the division lemma to get
281 = 170 x 1 + 111
We consider the new divisor 170 and the new remainder 111,and apply the division lemma to get
170 = 111 x 1 + 59
We consider the new divisor 111 and the new remainder 59,and apply the division lemma to get
111 = 59 x 1 + 52
We consider the new divisor 59 and the new remainder 52,and apply the division lemma to get
59 = 52 x 1 + 7
We consider the new divisor 52 and the new remainder 7,and apply the division lemma to get
52 = 7 x 7 + 3
We consider the new divisor 7 and the new remainder 3,and apply the division lemma to get
7 = 3 x 2 + 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 451 and 732 is 1
Notice that 1 = HCF(3,1) = HCF(7,3) = HCF(52,7) = HCF(59,52) = HCF(111,59) = HCF(170,111) = HCF(281,170) = HCF(451,281) = HCF(732,451) .
We can take hcf of as 1st numbers and next number as another number to apply in Euclidean lemma
Step 1: Since 974 > 1, we apply the division lemma to 974 and 1, to get
974 = 1 x 974 + 0
The remainder has now become zero, so our procedure stops. Since the divisor at this stage is 1, the HCF of 1 and 974 is 1
Notice that 1 = HCF(974,1) .
We can take hcf of as 1st numbers and next number as another number to apply in Euclidean lemma
Step 1: Since 406 > 1, we apply the division lemma to 406 and 1, to get
406 = 1 x 406 + 0
The remainder has now become zero, so our procedure stops. Since the divisor at this stage is 1, the HCF of 1 and 406 is 1
Notice that 1 = HCF(406,1) .
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Frequently Asked Questions on HCF of 451, 732, 974, 406 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 451, 732, 974, 406?
Answer: HCF of 451, 732, 974, 406 is 1 the largest number that divides all the numbers leaving a remainder zero.
3. How to find HCF of 451, 732, 974, 406 using Euclid's Algorithm?
Answer: For arbitrary numbers 451, 732, 974, 406 apply Euclid’s Division Lemma in succession until you obtain a remainder zero. HCF is the remainder in the last but one step.