Highest Common Factor of 476, 749, 37 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 476, 749, 37 i.e. 1 the largest integer that leaves a remainder zero for all numbers.
HCF of 476, 749, 37 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 476, 749, 37 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 476, 749, 37 is 1.
HCF(476, 749, 37) = 1
HCF of 476, 749, 37 using Euclid's algorithm
Highest common factor or Highest common divisor (hcd) can be calculated by Euclid's algotithm.
Highest common factor (HCF) of 476, 749, 37 is 1.
Highest Common Factor of 476,749,37 is 1
Step 1: Since 749 > 476, we apply the division lemma to 749 and 476, to get
749 = 476 x 1 + 273
Step 2: Since the reminder 476 ≠ 0, we apply division lemma to 273 and 476, to get
476 = 273 x 1 + 203
Step 3: We consider the new divisor 273 and the new remainder 203, and apply the division lemma to get
273 = 203 x 1 + 70
We consider the new divisor 203 and the new remainder 70,and apply the division lemma to get
203 = 70 x 2 + 63
We consider the new divisor 70 and the new remainder 63,and apply the division lemma to get
70 = 63 x 1 + 7
We consider the new divisor 63 and the new remainder 7,and apply the division lemma to get
63 = 7 x 9 + 0
The remainder has now become zero, so our procedure stops. Since the divisor at this stage is 7, the HCF of 476 and 749 is 7
Notice that 7 = HCF(63,7) = HCF(70,63) = HCF(203,70) = HCF(273,203) = HCF(476,273) = HCF(749,476) .
We can take hcf of as 1st numbers and next number as another number to apply in Euclidean lemma
Step 1: Since 37 > 7, we apply the division lemma to 37 and 7, to get
37 = 7 x 5 + 2
Step 2: Since the reminder 7 ≠ 0, we apply division lemma to 2 and 7, to get
7 = 2 x 3 + 1
Step 3: We consider the new divisor 2 and the new remainder 1, and apply the division lemma to get
2 = 1 x 2 + 0
The remainder has now become zero, so our procedure stops. Since the divisor at this stage is 1, the HCF of 7 and 37 is 1
Notice that 1 = HCF(2,1) = HCF(7,2) = HCF(37,7) .
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Frequently Asked Questions on HCF of 476, 749, 37 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 476, 749, 37?
Answer: HCF of 476, 749, 37 is 1 the largest number that divides all the numbers leaving a remainder zero.
3. How to find HCF of 476, 749, 37 using Euclid's Algorithm?
Answer: For arbitrary numbers 476, 749, 37 apply Euclid’s Division Lemma in succession until you obtain a remainder zero. HCF is the remainder in the last but one step.