Highest Common Factor of 440, 714, 374 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 440, 714, 374 i.e. 2 the largest integer that leaves a remainder zero for all numbers.
HCF of 440, 714, 374 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 440, 714, 374 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 440, 714, 374 is 2.
HCF(440, 714, 374) = 2
HCF of 440, 714, 374 using Euclid's algorithm
Highest common factor or Highest common divisor (hcd) can be calculated by Euclid's algotithm.
Highest common factor (HCF) of 440, 714, 374 is 2.
Highest Common Factor of 440,714,374 is 2
Step 1: Since 714 > 440, we apply the division lemma to 714 and 440, to get
714 = 440 x 1 + 274
Step 2: Since the reminder 440 ≠ 0, we apply division lemma to 274 and 440, to get
440 = 274 x 1 + 166
Step 3: We consider the new divisor 274 and the new remainder 166, and apply the division lemma to get
274 = 166 x 1 + 108
We consider the new divisor 166 and the new remainder 108,and apply the division lemma to get
166 = 108 x 1 + 58
We consider the new divisor 108 and the new remainder 58,and apply the division lemma to get
108 = 58 x 1 + 50
We consider the new divisor 58 and the new remainder 50,and apply the division lemma to get
58 = 50 x 1 + 8
We consider the new divisor 50 and the new remainder 8,and apply the division lemma to get
50 = 8 x 6 + 2
We consider the new divisor 8 and the new remainder 2,and apply the division lemma to get
8 = 2 x 4 + 0
The remainder has now become zero, so our procedure stops. Since the divisor at this stage is 2, the HCF of 440 and 714 is 2
Notice that 2 = HCF(8,2) = HCF(50,8) = HCF(58,50) = HCF(108,58) = HCF(166,108) = HCF(274,166) = HCF(440,274) = HCF(714,440) .
We can take hcf of as 1st numbers and next number as another number to apply in Euclidean lemma
Step 1: Since 374 > 2, we apply the division lemma to 374 and 2, to get
374 = 2 x 187 + 0
The remainder has now become zero, so our procedure stops. Since the divisor at this stage is 2, the HCF of 2 and 374 is 2
Notice that 2 = HCF(374,2) .
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Frequently Asked Questions on HCF of 440, 714, 374 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 440, 714, 374?
Answer: HCF of 440, 714, 374 is 2 the largest number that divides all the numbers leaving a remainder zero.
3. How to find HCF of 440, 714, 374 using Euclid's Algorithm?
Answer: For arbitrary numbers 440, 714, 374 apply Euclid’s Division Lemma in succession until you obtain a remainder zero. HCF is the remainder in the last but one step.